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Common Core: High School - Algebra : Creating Equations✭

Study concepts, example questions & explanations for Common Core: High School - Algebra

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All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

There are 6 apples in a small fruit basket and 10 apples in a large fruit basket. If Sally buys a total of 5 fruit baskets that has a combined total of 34 apples, write a system of equation that represents Sally's situation.

Possible Answers:

$\\6s+10l=34 \\s+l=5$

$\\6s+10l=34 \\4s+l=5$

$\\6s+10l=34 \\s+4l=5$

$\\6s+10l=34 \\2s+l=5$

$\\6s+10l=34 \\s+2l=5$

Correct answer:

$\\6s+10l=34 \\s+l=5$

Explanation:

To write the appropriate equation for this situation, start by identifying what is known.

$\\\text{small fruit basket}=6\text{ apples} \\\text{large fruit basket}=10\text{ apples}$

Now write the equation in words.

$\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=34\text{ apples}$

Let

$\\s=\text{small fruit basket} \\l=\text{large fruit basket}$

therefore the equation becomes,

6s+10l=34

Now, since there are 5 fruit baskets set up another equation.

$\\\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=5\text{ baskets} \\s+l=5$

From here set up the system of equation for this situation.

$\\6s+10l=34 \\s+l=5$

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Example Question #2 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

There are 3 apples in a small fruit basket and 7 apples in a large fruit basket. If Sally buys a total of 5 fruit baskets that have a combined total of 31 apples, write a system of equations that represents Sally's situation.

Possible Answers:

$\\3s+7l=31 \\s+4l=5$

$\\3s+7l=31 \\4s+l=5$

$\\3s+7l=31 \\s+l=5$

$\\3s+7l=5 \\s+l=31$

$\\3s+7l=31 \\2s+3l=5$

Correct answer:

$\\3s+7l=31 \\s+l=5$

Explanation:

To write the appropriate equation for this situation, start by identifying what is known.

$\\\text{small fruit basket}=3\text{ apples} \\\text{large fruit basket}=7\text{ apples}$

Now write the equation in words.

$\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=31\text{ apples}$

Let

$\\s=\text{small fruit basket} \\l=\text{large fruit basket}$

therefore the equation becomes,

3s+7l=31

Now, since there are 5 fruit baskets set up another equation.

$\\\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=5\text{ baskets} \\s+l=5$

From here set up the system of equation for this situation.

$\\3s+7l=31 \\s+l=5$

Report an Error

Example Question #1 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

There are 5 apples in a small fruit basket and 10 apples in a large fruit basket. If Sally buys a total of 5 fruit baskets that have a combined total of 40 apples, write a system of equations that describes Sally's situation.

Possible Answers:

$\\5s+l=40 \\s+l=5$

$\\s+10l=40 \\s+l=5$

$\\5s+10l=40 \\3s+l=5$

$\\5s+10l=40 \\s+l=5$

$\\5s+10l=40 \\s+2l=5$

Correct answer:

$\\5s+10l=40 \\s+l=5$

Explanation:

To write the appropriate equation for this situation, start by identifying what is known.

$\\\text{small fruit basket}=5\text{ apples} \\\text{large fruit basket}=10\text{ apples}$

Now write the equation in words.

$\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=40\text{ apples}$

Let

$\\s=\text{small fruit basket} \\l=\text{large fruit basket}$

therefore the equation becomes,

5s+10l=40

Now, since there are 5 fruit baskets set up another equation.

$\\\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=5\text{ baskets} \\s+l=5$

From here set up the system of equation for this situation.

$\\5s+10l=40 \\s+l=5$

Report an Error

Example Question #1 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

There are 15 apples in a small fruit basket and 20 apples in a large fruit basket. If Sally buys a total of 5 fruit baskets that have a combined total of 95 apples, write a system of equations that represents Sally's situation.

Possible Answers:

$\\5s+20l=95 \\s+l=5$

$\\15s+20l=95 \\s+4l=5$

$\\15s+20l=95 \\s+l=5$

$\\15s+20l=95 \\s+2l=5$

$\\15s+20l=95 \\3s+l=5$

Correct answer:

$\\15s+20l=95 \\s+l=5$

Explanation:

To write the appropriate equation for this situation, start by identifying what is known.

$\\\text{small fruit basket}=15\text{ apples} \\\text{large fruit basket}=20\text{ apples}$

Now write the equation in words.

$\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=95\text{ apples}$

Let

$\\s=\text{small fruit basket} \\l=\text{large fruit basket}$

therefore the equation becomes,

15s+20l=95

Now, since there are 5 fruit baskets set up another equation.

$\\\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=5\text{ baskets} \\s+l=5$

From here set up the system of equation for this situation.

$\\15s+20l=95 \\s+l=5$

Report an Error

Example Question #11 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

There are 5 apples in a small fruit basket and 10 apples in a large fruit basket. If Sally buys a total of 5 fruit baskets that have a combined total of 40 apples, how many small baskets does Sally have?

Possible Answers:

s=2

s=5

s=1

s=4

s=3

Correct answer:

s=2

Explanation:

To write the appropriate equation for this situation, start by identifying what is known.

$\\\text{small fruit basket}=5\text{ apples} \\\text{large fruit basket}=10\text{ apples}$

Now write the equation in words.

$\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=40\text{ apples}$

Let

$\\s=\text{small fruit basket} \\l=\text{large fruit basket}$

therefore the equation becomes,

5s+10l=40

Now, since there are 5 fruit baskets set up another equation.

$\\\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=5\text{ baskets} \\s+l=5$

From here set up the system of equation for this situation.

$\\5s+10l=40 \\s+l=5$

Now, solve the second equation for .

$\\s+l=5 \\s=5-l$

Substitute this into the first equation.

$\\5s+10l=40 \\5(5-l)+10l=40 \\25-5l+10l=40 \\25+5l=40 \\5l=15 \\l=3$

Now substitute this value into the second equation to solve for .

$\\s+l=5 \\s=5-3\\s=2$

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Example Question #441 : High School: Algebra

There are 5 apples in a small fruit basket and 10 apples in a large fruit basket. If Sally buys a total of 5 fruit baskets that have a combined total of 40 apples, how many large baskets does Sally have?

Possible Answers:

l=2

l=5

l=3

l=1

l=4

Correct answer:

l=3

Explanation:

To write the appropriate equation for this situation, start by identifying what is known.

$\\\text{small fruit basket}=5\text{ apples} \\\text{large fruit basket}=10\text{ apples}$

Now write the equation in words.

$\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=40\text{ apples}$

Let

$\\s=\text{small fruit basket} \\l=\text{large fruit basket}$

therefore the equation becomes,

5s+10l=40

Now, since there are 5 fruit baskets set up another equation.

$\\\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=5\text{ baskets} \\s+l=5$

From here set up the system of equation for this situation.

$\\5s+10l=40 \\s+l=5$

Now, solve the second equation for .

$\\s+l=5 \\s=5-l$

Substitute this into the first equation.

$\\5s+10l=40 \\5(5-l)+10l=40 \\25-5l+10l=40 \\25+5l=40 \\5l=15 \\l=3$

Report an Error

Example Question #31 : Creating Equations✭

To calculate the slope of a line, the following formula is used.

$m=\frac{y_2-y_1}{x_2-x_1}$

Solve this equation for y_2 .

Possible Answers:

y_2=(x_2-x_1)m

y_2=x_2-x_1m+y_1

y_2=(x_2-x_1)m+y_1

y_2=(x_2-x_1)+y_1m

y_2=x_2m-x_1+y_1

Correct answer:

y_2=(x_2-x_1)m+y_1

Explanation:

This question is asking to rearrange the slope formula to highlight a quantity of interest, specifically y_2 .

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

First, multiply both sides by the quantity (x_2-x_1) in order to move it from the right side of the equation to the left side. Performing the opposite operation allows for rearranging to occur.

$\\(x_2-x_1)\cdot m=\frac{y_2-y_1}{x_2-x_1}\cdot (x_2-x_1) \\\\(x_2-x_1)m=y_2-y_1$

Next, add y_1 to both sides of the equation.

$\\(x_2-x_1)m+y_1=y_2-y_1+y_1 \\(x_2-x_1)m+y_1=y_2$

Therefore, the equation solved for y_2 is

y_2=(x_2-x_1)m+y_1

Report an Error

Example Question #32 : Creating Equations✭

To calculate the slope of a line, the following formula is used.

$m=\frac{y_2-y_1}{x_2-x_1}$

Solve this equation for y_1 .

Possible Answers:

y_1=-(x_2-x_1)m+y_2m

y_1=-(x_2-x_1)m+y_2

y_1=-(x_2-x_1)m-y_2

y_1=(x_2-x_1)m+y_2

y_1=(x_2-x_1)m-y_2

Correct answer:

y_1=-(x_2-x_1)m+y_2

Explanation:

This question is asking to rearrange the slope formula to highlight a quantity of interest, specifically y_1 .

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

First, multiply both sides by the quantity (x_2-x_1) in order to move it from the right side of the equation to the left side. Performing the opposite operation allows for rearranging to occur.

$\\(x_2-x_1)\cdot m=\frac{y_2-y_1}{x_2-x_1}\cdot (x_2-x_1) \\\\(x_2-x_1)m=y_2-y_1$

Next, subtract y_2 to both sides of the equation.

$\\(x_2-x_1)m-y_2=y_2-y_1-y_2 \\(x_2-x_1)m-y_2=-y_1$

Now, divide by negative one on both sides.

$\frac{(x_2-x_1)m-y_2}{-1}=-\frac{y_1}{-1}$

-(x_2-x_1)m+y_2=y_1

Therefore, the equation solved for y_1 is,

y_1=-(x_2-x_1)m+y_2

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Example Question #33 : Creating Equations✭

To calculate the slope of a line, the following formula is used.

$m=\frac{y_2-y_1}{x_2-x_1}$

Solve this equation for x_2

Possible Answers:

$x_2=\frac{y_2+y_1}{m}+x_1$

$x_2=-\frac{y_2-y_1}{m}+x_1$

$x_2=\frac{y_2-y_1}{m}+x_1$

$x_2=\frac{y_2-y_1}{m}-x_1$

$x_2=-\frac{y_2-y_1}{m}-x_1$

Correct answer:

$x_2=\frac{y_2-y_1}{m}+x_1$

Explanation:

This question is asking to rearrange the slope formula to highlight a quantity of interest, specifically x_2 .

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

First, multiply both sides by the quantity (x_2-x_1) in order to move it from the right side of the equation to the left side. Performing the opposite operation allows for rearranging to occur.

$\\(x_2-x_1)\cdot m=\frac{y_2-y_1}{x_2-x_1}\cdot (x_2-x_1) \\\\(x_2-x_1)m=y_2-y_1$

Next divide by on both sides.

$\frac{(x_2-x_1)m}{m}=\frac{y_2-y_1}{m}$

$x_2-x_1=\frac{y_2-y_1}{m}$

Now add x_1 to both sides.

$x_2-x_1+x_1=\frac{y_2-y_1}{m}+x_1$

$x_2=\frac{y_2-y_1}{m}+x_1$

Report an Error

Example Question #34 : Creating Equations✭

To calculate the slope of a line, the following formula is used.

$m=\frac{y_2-y_1}{x_2-x_1}$

Solve this equation for x_1 .

Possible Answers:

$x_1=\frac{y_2-y_1}{m}+x_2$

$x_1=\frac{y_2-y_1}{m}-x_2$

$x_1=-\frac{y_2+y_1}{m}+x_2$

$x_1=-\frac{y_2-y_1}{m}-x_2$

$x_1=-\frac{y_2-y_1}{m}+x_2$

Correct answer:

$x_1=-\frac{y_2-y_1}{m}+x_2$

Explanation:

This question is asking to rearrange the slope formula to highlight a quantity of interest, specifically x_1 .

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

First, multiply both sides by the quantity (x_2-x_1) in order to move it from the right side of the equation to the left side. Performing the opposite operation allows for rearranging to occur.

$\\(x_2-x_1)\cdot m=\frac{y_2-y_1}{x_2-x_1}\cdot (x_2-x_1) \\\\(x_2-x_1)m=y_2-y_1$

Next divide by on both sides.

$\frac{(x_2-x_1)m}{m}=\frac{y_2-y_1}{m}$

$x_2-x_1=\frac{y_2-y_1}{m}$

Now subtract x_2 from both sides.

$x_2-x_1-x_2=\frac{y_2-y_1}{m}-x_2$

$-x_1=\frac{y_2-y_1}{m}-x_2$

Finally, divide by negative one.

$x_1=-\frac{y_2-y_1}{m}+x_2$

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All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

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Common Core: High School - Algebra : Creating Equations✭

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #1 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

Example Question #2 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

Example Question #1 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

Example Question #1 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

Example Question #11 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

Example Question #441 : High School: Algebra

Example Question #31 : Creating Equations✭

Example Question #32 : Creating Equations✭

Example Question #33 : Creating Equations✭

Example Question #34 : Creating Equations✭

All Common Core: High School - Algebra Resources

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