Pick any number to be the original diameter. 10 is easy to work with. If the diameter is 10, the radius is 5. The area of the original image is A = πr², so the original area = 25π. Now we increase the diameter by 75%, so the new diameter is 17.5. The radius is then 8.75. The area of the enlarged image is approximately 77π. To find the percentage by which the area has increased, take the difference in areas divided by the original area.  (77π - 25π)/25π = 51π/25π = 51/25 = 2.04 or approximately 200%

The area of a square is given by , and if the side is doubled, the new area becomes .  The increase is a factor of 4, which is 400%.

The equation to use for percent increase or decrease is 

to find the change in area, let's first calculate the area of the original. The formula for area of a rectangle is area=length x width. The original area, therefore, is . 

The new rectangle has side lengths which are increased by 2, so the new lengths are 8 and 12. The area of the new rectangle, then is .

The change in area is found by subtracting the the old area from the new area, so . 

When you input these numbers into the percent increase equation, you get

We are told that 20% of x is equal to 160% of y. We need to write expressions for 20% of x and 160% of y and set them equal to one another.

In order to find an expression for 20% of x, we can write 20% as a decimal and multiply it by x. Since 20% = 0.20, we can write 20% of x as 0.2x.

Similarly, we can write 160% as 1.60y.

Now, we set these expressions equal to one another.

0.2x = 1.60y.

Since the question asks us to find y as a percentage of x, we need to solve for y in terms of x. Let's divide both sides of the equation by 1.60.

0.125x = y.

Therfore, y is equal to 0.125x, which is the same as 12.5% of x, since 12.5% expressed as a decimal is 0.125.

The answer is 12.5. 

Move the decimal two places to the left to convert a decimal to a percentage. Therefore, .789 is equivalent to 78.9%.

55 and 1/2% can be written as a decimal: 0.555. To see what number is about 55.5% of 23, multiply 0.555 by 23. Answer: 12.765 or about 13.

Another route is to say that 55.5% is about half of 23. Half of 23 is 11.5. Since 55.5% is greater than 50%, 13 is the logical choice instead of 11.

We need to find expressions for fifty percent of x and for thirty percent of the positive difference between x and y. Then, we can set these two expressions equal to each other and determine the ratio of x to y.

Fifty percent of x is equal to one-half of x, which is the same as multiplying x by 0.50.

50% of x = 0.5x

Thirty percent of the positive difference between x and y means that we need to multiply the positive difference between x and y by thirty percent. Because x > y, the positive difference between x and y is equal to x – y. We then need to take thirty percent of the quantity x – y. Remember that to convert from a percent to a decimal, we move the decimal two spaces to the left. Therefore, 30% = 0.30. We can now multiply this by (x – y).

30% of x – y = 0.30(x – y)

Now, we set the two expressions equal to one another.

0.5x = 0.30(x – y)

Distribute the right side.

0.5x = 0.3x – 0.3y

The ratio of x to y is represent by x/y. Thus, we want to group the x and y terms on opposite sides of the equations, and then divide both sides by y.

0.5x = 0.3x – 0.3y

Subtract 0.3x from both sides.

0.2x = –0.3y

Divide both sides by 0.2

x = (–0.3/0.2)y

Divide both sides by y to find x/y.

x/y = (–0.3/0.2) = –1.5.

Because the answers are in fractions, we want to rewrite –1.5 as a fraction. We can write –1.5 as –1.5/1 and then mutiply the top and bottom by 2.

(–1.5/1)(2/2) = –3/2

The answer is –3/2

We are told that 50% of x is equal to 25% of y. We need to represent these two pieces of information as algebraic expressions. We can convert 50% and 25% to decimals by moving the decimals two places to the left. Thus, 50% = 0.50, and 25% = 0.25. To find 50% of x, we multiply x by 0.50. In other words, 50% of x = 0.50x. Likewise, 25% of y = 0.25y. We now set 0.50x and 0.25y equal to one another.

0.50x = 0.25y

Let's divide both sides by 0.25 to get rid of decimals.

2x = y

Next, we are told that 40% of y is equal to 60% of z. We will represent 40% and 60% as 0.40 and 0.60, respectively. Thus, we can write the following equation:

0.40y = 0.60z

Ultimately, we are asked to find x as a percentage of z. This means we want to find an equation with x and z, but not y. If we solve for y in the second equation, and then substitute this value into the first, we can eliminate y.

Let's take the equation 0.40y = 0.60z and divide both sides by 0.40.

y = 1.5z

Now, we can take 1.5z and substitute this for y in the first equation.

2x = 1.5z

In order to find x as a percent of z, we must solve for x in terms of z. This means we must divide both sides of the equation by 2.

x = 0.75z

x is 0.75 times z. We can represent 0.75 as 75%, because in order to convert from a decimal to a percent, we need to move the decimal two spaces to the right. Therefore, if x = 0.75z, then x = 75% of z.

The answer is 75.

In order to answer the question, we must find out the percent of each class that has signed Tom's petition, and compare it to 8%.

Freshmen:   have signed.

Sophomores:  have signed.

Juniors:  have signed.

Seniors:  have signed.

Tom has the necessary signatures from members of the top three classes, but he cannot get on the ballot yet because he has not gathered enough signatures from freshmen.

22% = 22/100

Divide everything by 2:

22/100 = 11/50

11 is a prime number, so this is as reduced as this fraction can get.