How to find the whole from the part - PSAT Math

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Question

Mr. Owens spent $7.50 for a dinner buffet. The amount he paid accounted for 3/4 of the money in his wallet. How much money is left in his wallet for other expenses?

Answer

If $7.50 is 3/4 of the total, 7.50/3 gives us what 1/4 of his total money would be. This equals $2.50, the remaining unspent quarter.

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Question

A certain ball that is dropped will bounce back to 3/5 of the height it was initially dropped from. If after the 2nd bounce the ball reaches 39.96 ft, what was the initial height the ball was dropped from?

Answer

We know the height of the initial bounce, so work backwards to find the initial height. 39.96/0.6 = 66.6 = height of ball after first bounce

66.6/0.6 = 111 ft

Compare your answer with the correct one above

Question

If Mr. Jones’ math class has 8 boys and two-thirds of the class are girls, how many total students are in the class?

Answer

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class:

8 = (1/3) x, where x is the number in the entire class.

When we solve for x in the equation we get x = 24.

Compare your answer with the correct one above

Question

A pitcher of water is filled $\dpi{100} \small \frac{2}{5}$ of full. An additional 27 ounces of water is added. Now the pitcher of water is completely full. How much water does the pitcher hold?

Answer

If $\dpi{100} \small 27$ ounces fills the pitcher, then it must equal the volume of $\dpi{100} \small \frac{3}{5}$ of the pitcher. If $\dpi{100} \small \frac{3}{5}$ of a pitcher equals 27 ounces, then $\dpi{100} \small \frac{1}{5}$ of a pitcher equals $\dpi{100} \small 27\div 3=9$ ounces. Since there are $\dpi{100} \small 5$ fifths in the pitcher, it must hold $\dpi{100} \small 9\times 5=45$ ounces total.

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Question

A certain bakery makes chocolate, vanilla, red velvet, and carrot cupcakes in a ratio of 2:3:5:1. If that bakery makes 63 vanilla cupcakes in one day, what is the total number of cupcakes that the bakery made that day?

Answer

Because the bakery makes 63 vanilla cupcakes in one day, start by dividing the 63 by the vanilla part of the ratio, which is 3. $63\div3=21$ . That means that the bakery made 21 times the basic set of 2 chocolate, 3 vanilla, 5 red velvet, and 1 carrot cupcakes.

Now add up the parts of your ratio: . If the bakery only made 3 vanilla cupcakes, then it would have made 11 cupcakes that day. But, because the bakery made 21 times that number of vanilla cupcakes, it made 21 times the total number of cupcakes over the course of the day. To find the total number of cupcakes the bakery made that day, you multiply $21\times11$ to get .

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Question

A circle is divided into various sized slices. One slice has an interior angle of $40^\circ$ and an area of $9\pi$ . What is the circumference of the circle?

Answer

In order to find the circumference of the cirlce, we will need to find the radius of the circle. We know that a slice with a 40-degree angle has an area of $9\pi$ . There are 360 degrees in a circle. Therefore, the slice of the circle with an angle of 40 dgrees is one-ninth of the entire circle.

Multiply $9\pi$ by 9 to find the area of the circle

$=9\pi\cdot9$

$=81\pi$

The area of the circle is $81\pi$ . Now use the formula for area to find the radius

$A=\pi r^2$

$81\pi=\pi r^2$

The radius of the circle is 9. Use the formula for circumference to find the circumference of the circle:

$C=2\pi r$

$C=2\pi (9)$

$C=18\pi$

The circumference of the circle is $18\pi$ .

Compare your answer with the correct one above

Question

If Mr. Jones’ math class has 8 boys and two-thirds of the class are girls, how many total students are in the class?

Answer

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class:

8 = (1/3) x, where x is the number in the entire class.

When we solve for x in the equation we get x = 24.

Compare your answer with the correct one above

Question

Mr. Owens spent $7.50 for a dinner buffet. The amount he paid accounted for 3/4 of the money in his wallet. How much money is left in his wallet for other expenses?

Answer

If $7.50 is 3/4 of the total, 7.50/3 gives us what 1/4 of his total money would be. This equals $2.50, the remaining unspent quarter.

Compare your answer with the correct one above

Question

A certain ball that is dropped will bounce back to 3/5 of the height it was initially dropped from. If after the 2nd bounce the ball reaches 39.96 ft, what was the initial height the ball was dropped from?

Answer

We know the height of the initial bounce, so work backwards to find the initial height. 39.96/0.6 = 66.6 = height of ball after first bounce

66.6/0.6 = 111 ft

Compare your answer with the correct one above

Question

A pitcher of water is filled $\dpi{100} \small \frac{2}{5}$ of full. An additional 27 ounces of water is added. Now the pitcher of water is completely full. How much water does the pitcher hold?

Answer

If $\dpi{100} \small 27$ ounces fills the pitcher, then it must equal the volume of $\dpi{100} \small \frac{3}{5}$ of the pitcher. If $\dpi{100} \small \frac{3}{5}$ of a pitcher equals 27 ounces, then $\dpi{100} \small \frac{1}{5}$ of a pitcher equals $\dpi{100} \small 27\div 3=9$ ounces. Since there are $\dpi{100} \small 5$ fifths in the pitcher, it must hold $\dpi{100} \small 9\times 5=45$ ounces total.

Compare your answer with the correct one above

Question

A certain bakery makes chocolate, vanilla, red velvet, and carrot cupcakes in a ratio of 2:3:5:1. If that bakery makes 63 vanilla cupcakes in one day, what is the total number of cupcakes that the bakery made that day?

Answer

Because the bakery makes 63 vanilla cupcakes in one day, start by dividing the 63 by the vanilla part of the ratio, which is 3. $63\div3=21$ . That means that the bakery made 21 times the basic set of 2 chocolate, 3 vanilla, 5 red velvet, and 1 carrot cupcakes.

Now add up the parts of your ratio: . If the bakery only made 3 vanilla cupcakes, then it would have made 11 cupcakes that day. But, because the bakery made 21 times that number of vanilla cupcakes, it made 21 times the total number of cupcakes over the course of the day. To find the total number of cupcakes the bakery made that day, you multiply $21\times11$ to get .

Compare your answer with the correct one above

Question

A circle is divided into various sized slices. One slice has an interior angle of $40^\circ$ and an area of $9\pi$ . What is the circumference of the circle?

Answer

In order to find the circumference of the cirlce, we will need to find the radius of the circle. We know that a slice with a 40-degree angle has an area of $9\pi$ . There are 360 degrees in a circle. Therefore, the slice of the circle with an angle of 40 dgrees is one-ninth of the entire circle.

Multiply $9\pi$ by 9 to find the area of the circle

$=9\pi\cdot9$

$=81\pi$

The area of the circle is $81\pi$ . Now use the formula for area to find the radius

$A=\pi r^2$

$81\pi=\pi r^2$

The radius of the circle is 9. Use the formula for circumference to find the circumference of the circle:

$C=2\pi r$

$C=2\pi (9)$

$C=18\pi$

The circumference of the circle is $18\pi$ .

Compare your answer with the correct one above

Question

If Mr. Jones’ math class has 8 boys and two-thirds of the class are girls, how many total students are in the class?

Answer

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class:

8 = (1/3) x, where x is the number in the entire class.

When we solve for x in the equation we get x = 24.

Compare your answer with the correct one above

Question

Mr. Owens spent $7.50 for a dinner buffet. The amount he paid accounted for 3/4 of the money in his wallet. How much money is left in his wallet for other expenses?

Answer

If $7.50 is 3/4 of the total, 7.50/3 gives us what 1/4 of his total money would be. This equals $2.50, the remaining unspent quarter.

Compare your answer with the correct one above

Question

A certain ball that is dropped will bounce back to 3/5 of the height it was initially dropped from. If after the 2nd bounce the ball reaches 39.96 ft, what was the initial height the ball was dropped from?

Answer

We know the height of the initial bounce, so work backwards to find the initial height. 39.96/0.6 = 66.6 = height of ball after first bounce

66.6/0.6 = 111 ft

Compare your answer with the correct one above

Question

A pitcher of water is filled $\dpi{100} \small \frac{2}{5}$ of full. An additional 27 ounces of water is added. Now the pitcher of water is completely full. How much water does the pitcher hold?

Answer

If $\dpi{100} \small 27$ ounces fills the pitcher, then it must equal the volume of $\dpi{100} \small \frac{3}{5}$ of the pitcher. If $\dpi{100} \small \frac{3}{5}$ of a pitcher equals 27 ounces, then $\dpi{100} \small \frac{1}{5}$ of a pitcher equals $\dpi{100} \small 27\div 3=9$ ounces. Since there are $\dpi{100} \small 5$ fifths in the pitcher, it must hold $\dpi{100} \small 9\times 5=45$ ounces total.

Compare your answer with the correct one above

Question

A certain bakery makes chocolate, vanilla, red velvet, and carrot cupcakes in a ratio of 2:3:5:1. If that bakery makes 63 vanilla cupcakes in one day, what is the total number of cupcakes that the bakery made that day?

Answer

Because the bakery makes 63 vanilla cupcakes in one day, start by dividing the 63 by the vanilla part of the ratio, which is 3. $63\div3=21$ . That means that the bakery made 21 times the basic set of 2 chocolate, 3 vanilla, 5 red velvet, and 1 carrot cupcakes.

Now add up the parts of your ratio: . If the bakery only made 3 vanilla cupcakes, then it would have made 11 cupcakes that day. But, because the bakery made 21 times that number of vanilla cupcakes, it made 21 times the total number of cupcakes over the course of the day. To find the total number of cupcakes the bakery made that day, you multiply $21\times11$ to get .

Compare your answer with the correct one above

Question

A circle is divided into various sized slices. One slice has an interior angle of $40^\circ$ and an area of $9\pi$ . What is the circumference of the circle?

Answer

In order to find the circumference of the cirlce, we will need to find the radius of the circle. We know that a slice with a 40-degree angle has an area of $9\pi$ . There are 360 degrees in a circle. Therefore, the slice of the circle with an angle of 40 dgrees is one-ninth of the entire circle.

Multiply $9\pi$ by 9 to find the area of the circle

$=9\pi\cdot9$

$=81\pi$

The area of the circle is $81\pi$ . Now use the formula for area to find the radius

$A=\pi r^2$

$81\pi=\pi r^2$

The radius of the circle is 9. Use the formula for circumference to find the circumference of the circle:

$C=2\pi r$

$C=2\pi (9)$

$C=18\pi$

The circumference of the circle is $18\pi$ .

Compare your answer with the correct one above

Question

If Mr. Jones’ math class has 8 boys and two-thirds of the class are girls, how many total students are in the class?

Answer

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class:

8 = (1/3) x, where x is the number in the entire class.

When we solve for x in the equation we get x = 24.

Compare your answer with the correct one above

Question

Mr. Owens spent $7.50 for a dinner buffet. The amount he paid accounted for 3/4 of the money in his wallet. How much money is left in his wallet for other expenses?

Answer

If $7.50 is 3/4 of the total, 7.50/3 gives us what 1/4 of his total money would be. This equals $2.50, the remaining unspent quarter.

Compare your answer with the correct one above

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How to find the whole from the part - PSAT Math

Mr. Owens spent $7.50 for a dinner buffet. The amount he paid accounted for 3/4 of the money in his wallet. How much money is left in his wallet for other expenses?

If $7.50 is 3/4 of the total, 7.50/3 gives us what 1/4 of his total money would be. This equals $2.50, the remaining unspent quarter.

A certain ball that is dropped will bounce back to 3/5 of the height it was initially dropped from. If after the 2nd bounce the ball reaches 39.96 ft, what was the initial height the ball was dropped from?

We know the height of the initial bounce, so work backwards to find the initial height. 39.96/0.6 = 66.6 = height of ball after first bounce 66.6/0.6 = 111 ft

If Mr. Jones’ math class has 8 boys and two-thirds of the class are girls, how many total students are in the class?

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class: 8 = (1/3) x, where x is the number in the entire class. When we solve for x in the equation we get x = 24.

A pitcher of water is filled of full. An additional 27 ounces of water is added. Now the pitcher of water is completely full. How much water does the pitcher hold?

If ounces fills the pitcher, then it must equal the volume of of the pitcher. If of a pitcher equals 27 ounces, then of a pitcher equals ounces. Since there are fifths in the pitcher, it must hold ounces total.

A certain bakery makes chocolate, vanilla, red velvet, and carrot cupcakes in a ratio of 2:3:5:1. If that bakery makes 63 vanilla cupcakes in one day, what is the total number of cupcakes that the bakery made that day?

A circle is divided into various sized slices. One slice has an interior angle of and an area of . What is the circumference of the circle?

If Mr. Jones’ math class has 8 boys and two-thirds of the class are girls, how many total students are in the class?

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class: 8 = (1/3) x, where x is the number in the entire class. When we solve for x in the equation we get x = 24.

Mr. Owens spent $7.50 for a dinner buffet. The amount he paid accounted for 3/4 of the money in his wallet. How much money is left in his wallet for other expenses?

If $7.50 is 3/4 of the total, 7.50/3 gives us what 1/4 of his total money would be. This equals $2.50, the remaining unspent quarter.

A certain ball that is dropped will bounce back to 3/5 of the height it was initially dropped from. If after the 2nd bounce the ball reaches 39.96 ft, what was the initial height the ball was dropped from?

We know the height of the initial bounce, so work backwards to find the initial height. 39.96/0.6 = 66.6 = height of ball after first bounce 66.6/0.6 = 111 ft

A pitcher of water is filled of full. An additional 27 ounces of water is added. Now the pitcher of water is completely full. How much water does the pitcher hold?

If ounces fills the pitcher, then it must equal the volume of of the pitcher. If of a pitcher equals 27 ounces, then of a pitcher equals ounces. Since there are fifths in the pitcher, it must hold ounces total.

A certain bakery makes chocolate, vanilla, red velvet, and carrot cupcakes in a ratio of 2:3:5:1. If that bakery makes 63 vanilla cupcakes in one day, what is the total number of cupcakes that the bakery made that day?

A circle is divided into various sized slices. One slice has an interior angle of and an area of . What is the circumference of the circle?

If Mr. Jones’ math class has 8 boys and two-thirds of the class are girls, how many total students are in the class?

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class: 8 = (1/3) x, where x is the number in the entire class. When we solve for x in the equation we get x = 24.

Mr. Owens spent $7.50 for a dinner buffet. The amount he paid accounted for 3/4 of the money in his wallet. How much money is left in his wallet for other expenses?

If $7.50 is 3/4 of the total, 7.50/3 gives us what 1/4 of his total money would be. This equals $2.50, the remaining unspent quarter.

A certain ball that is dropped will bounce back to 3/5 of the height it was initially dropped from. If after the 2nd bounce the ball reaches 39.96 ft, what was the initial height the ball was dropped from?

We know the height of the initial bounce, so work backwards to find the initial height. 39.96/0.6 = 66.6 = height of ball after first bounce 66.6/0.6 = 111 ft

A pitcher of water is filled of full. An additional 27 ounces of water is added. Now the pitcher of water is completely full. How much water does the pitcher hold?

If ounces fills the pitcher, then it must equal the volume of of the pitcher. If of a pitcher equals 27 ounces, then of a pitcher equals ounces. Since there are fifths in the pitcher, it must hold ounces total.

A certain bakery makes chocolate, vanilla, red velvet, and carrot cupcakes in a ratio of 2:3:5:1. If that bakery makes 63 vanilla cupcakes in one day, what is the total number of cupcakes that the bakery made that day?

A circle is divided into various sized slices. One slice has an interior angle of and an area of . What is the circumference of the circle?

If Mr. Jones’ math class has 8 boys and two-thirds of the class are girls, how many total students are in the class?

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class: 8 = (1/3) x, where x is the number in the entire class. When we solve for x in the equation we get x = 24.

Mr. Owens spent $7.50 for a dinner buffet. The amount he paid accounted for 3/4 of the money in his wallet. How much money is left in his wallet for other expenses?

If $7.50 is 3/4 of the total, 7.50/3 gives us what 1/4 of his total money would be. This equals $2.50, the remaining unspent quarter.

We know the height of the initial bounce, so work backwards to find the initial height. 39.96/0.6 = 66.6 = height of ball after first bounce

66.6/0.6 = 111 ft

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class:

8 = (1/3) x, where x is the number in the entire class.

When we solve for x in the equation we get x = 24.

A pitcher of water is filled $\dpi{100} \small \frac{2}{5}$ of full. An additional 27 ounces of water is added. Now the pitcher of water is completely full. How much water does the pitcher hold?

A circle is divided into various sized slices. One slice has an interior angle of $40^\circ$ and an area of $9\pi$ . What is the circumference of the circle?

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class:

8 = (1/3) x, where x is the number in the entire class.

When we solve for x in the equation we get x = 24.

We know the height of the initial bounce, so work backwards to find the initial height. 39.96/0.6 = 66.6 = height of ball after first bounce

66.6/0.6 = 111 ft

A pitcher of water is filled $\dpi{100} \small \frac{2}{5}$ of full. An additional 27 ounces of water is added. Now the pitcher of water is completely full. How much water does the pitcher hold?

A circle is divided into various sized slices. One slice has an interior angle of $40^\circ$ and an area of $9\pi$ . What is the circumference of the circle?

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class:

8 = (1/3) x, where x is the number in the entire class.

When we solve for x in the equation we get x = 24.

We know the height of the initial bounce, so work backwards to find the initial height. 39.96/0.6 = 66.6 = height of ball after first bounce

66.6/0.6 = 111 ft

A pitcher of water is filled $\dpi{100} \small \frac{2}{5}$ of full. An additional 27 ounces of water is added. Now the pitcher of water is completely full. How much water does the pitcher hold?

A circle is divided into various sized slices. One slice has an interior angle of $40^\circ$ and an area of $9\pi$ . What is the circumference of the circle?

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class:

8 = (1/3) x, where x is the number in the entire class.

When we solve for x in the equation we get x = 24.