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Common Core: High School - Algebra : Equations with Two or More Variables: CCSS.Math.Content.HSA-CED.A.2

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 #11 : Creating Equations✭

There are a total of 80 firefighters in a town. There are 4 fire departments in the town: North, South, East, and West. The North Department has 23 firefighters. The East Department has 13 firefighters. Let W represent the number of firefighters in the West Department and S represent the number of firefighters in the South Department. Which equation best illustrates this situation?

Possible Answers:

$\displaystyle 80=23+13+C$

$\displaystyle 80=23+W+S$

80=23+S $\displaystyle 80=23+S$

$\displaystyle 80=23+13+W+S$

$\displaystyle 80=13+W+S$

Correct answer:

$\displaystyle 80=23+13+W+S$

Explanation:

To find the equation that represents this particular situation, the word problem will need to be translated into mathematical terms.

There are 80 firefighters in the town. The North Department has 23 firefighters. The East Department has 13 firefighters. Let W represent the number of firefighters from the West Department and S the number of firefighters in the South Department.

This question is talking about the total firefighters in one town and each section of the town has a different fire department. In mathematical terms this looks as follows:

$\\\text{Total Town Firefighters}=\text{North Department + East Department + West Department + South Department} \\T=N+E+W+S$ $\displaystyle \\\text{Total Town Firefighters}=\text{North Department + East Department + West Department + South Department} \\T=N+E+W+S$

From here, identify the values for the known variables.

$\\T=80 \\N=23 \\E=13$ $\displaystyle \\T=80 \\N=23 \\E=13$

Substitute the values into the equation.

$\displaystyle 80=23+13+W+S$

Report an Error

Example Question #12 : Creating Equations✭

A candy shop contains a total of 300 items. There are 125 chocolates, 97 cookies, and T number of truffles. Write the equation that represents this situation.

Possible Answers:

$\displaystyle 300=125+97+T$

$\displaystyle 300=125+97T$

$\displaystyle 300=125T+97$

$\displaystyle 300=125+T$

$\displaystyle 300=97+T$

Correct answer:

$\displaystyle 300=125+97+T$

Explanation:

To find the equation that represents this particular situation, the word problem will need to be translated into mathematical terms.

A candy shop contains a total of 300 items. There are 125 chocolates, 97 cookies, and T number of truffles. In mathematical terms this looks as follows:

$\\\text{Total Candy Items}=\text{Chocolates + Cookies + Truffles} \\I=C+C_1+T$ $\displaystyle \\\text{Total Candy Items}=\text{Chocolates + Cookies + Truffles} \\I=C+C_1+T$

From here, identify the values for the known variables.

$\\I=300 \\C=125 \\C_1=97$ $\displaystyle \\I=300 \\C=125 \\C_1=97$

Substitute the values into the equation.

$\displaystyle 300=125+97+T$

Report an Error

Example Question #1 : Equations With Two Or More Variables: Ccss.Math.Content.Hsa Ced.A.2

A coffee shop made 50 drinks in the first hour of operation, 14 mochas, 10 lattes, and C number of hot chocolates. Write an equation that represents this situation.

Possible Answers:

$\displaystyle 50=14C+10$

$\displaystyle 50=14+10C$

$\displaystyle 50=14+10+C$

50=10+C $\displaystyle 50=10+C$

50=14+C $\displaystyle 50=14+C$

Correct answer:

$\displaystyle 50=14+10+C$

Explanation:

To find the equation that represents this particular situation, the word problem will need to be translated into mathematical terms.

A coffee shop made 50 drinks in the first hour of operation, 14 mochas, 10 lattes, and C number of hot chocolates. In mathematical terms this looks as follows:

$\\\text{Total Drinks}=\text{Mochas + Latte + Hot Chocolate} \\T=M+L+C$ $\displaystyle \\\text{Total Drinks}=\text{Mochas + Latte + Hot Chocolate} \\T=M+L+C$

From here, identify the values for the known variables.

$\\T=50 \\M=14 \\L=10$ $\displaystyle \\T=50 \\M=14 \\L=10$

Substitute the values into the equation.

$\displaystyle 50=14+10+C$

Report an Error

Example Question #2 : Equations With Two Or More Variables: Ccss.Math.Content.Hsa Ced.A.2

There are a total of 450 firefighters in a town. There are 4 fire departments in the town: North, South, East, and West. The North Department has 77 firefighters. The East Department has 21 firefighters. Let W represent the number of firefighters in the West Department and S represent the number of firefighters in the South Department. Which equation best illustrates this situation?

Possible Answers:

$\displaystyle 450=77+21+W$

$\displaystyle 450=21+W+S$

$\displaystyle 77=21+W+S$

$\displaystyle 450=77+21+W+S$

$\displaystyle 450=77+W+S$

Correct answer:

$\displaystyle 450=77+21+W+S$

Explanation:

To find the equation that represents this particular situation, the word problem will need to be translated into mathematical terms.

There are 450 firefighters in the town. The North Department has 77 firefighters. The East Department has 21 firefighters. Let W represent the number of firefighters from the West Department and S the number of firefighters in the South Department.

This question is talking about the total firefighters in one town and each section of the town has a different fire department. In mathematical terms this looks as follows:

From here, identify the values for the known variables.

$\\T=450 \\N=77 \\E=21$ $\displaystyle \\T=450 \\N=77 \\E=21$

Substitute the values into the equation.

$\displaystyle 450=77+21+W+S$

Report an Error

Example Question #1 : Equations With Two Or More Variables: Ccss.Math.Content.Hsa Ced.A.2

A candy shop contains a total of 100 items. There are 25 chocolates, 17 cookies, and T number of truffles. Write the equation that represents this situation.

Possible Answers:

$\displaystyle 100=25+T$

$\displaystyle 100=17+T$

25=17+T $\displaystyle 25=17+T$

$\displaystyle 120=25+17+T$

$\displaystyle 100=25+17+T$

Correct answer:

$\displaystyle 100=25+17+T$

Explanation:

To find the equation that represents this particular situation, the word problem will need to be translated into mathematical terms.

A candy shop contains a total of 100 items. There are 25 chocolates, 17 cookies, and T number of truffles. In mathematical terms this looks as follows:

$\\\text{Total Candy Items}=\text{Chocolates + Cookies + Truffles} \\I=C+C_1+T$ $\displaystyle \\\text{Total Candy Items}=\text{Chocolates + Cookies + Truffles} \\I=C+C_1+T$

From here, identify the values for the known variables.

$\\I=100 \\C=25 \\C_1=17$ $\displaystyle \\I=100 \\C=25 \\C_1=17$

Substitute the values into the equation.

$\displaystyle 100=25+17+T$

Report an Error

Example Question #13 : Creating Equations✭

A coffee shop made 150 drinks in the first hour of operation, 20 mochas, 10 lattes, and C number of hot chocolates. Write an equation that represents this situation.

Possible Answers:

$\displaystyle 150=10+C$

$\displaystyle 20=150+10+C$

$\displaystyle 150=20+10+C$

$\displaystyle 10=20+150+C$

$\displaystyle 150=20+C$

Correct answer:

$\displaystyle 150=20+10+C$

Explanation:

To find the equation that represents this particular situation, the word problem will need to be translated into mathematical terms.

A coffee shop made 150 drinks in the first hour of operation, 20 mochas, 10 lattes, and C number of hot chocolates. In mathematical terms this looks as follows:

$\\\text{Total Drinks}=\text{Mochas + Latte + Hot Chocolate} \\T=M+L+C$ $\displaystyle \\\text{Total Drinks}=\text{Mochas + Latte + Hot Chocolate} \\T=M+L+C$

From here, identify the values for the known variables.

$\\T=150 \\M=20 \\L=10$ $\displaystyle \\T=150 \\M=20 \\L=10$

Substitute the values into the equation.

$\displaystyle 150=20+10+C$

Report an Error

Example Question #2 : Equations With Two Or More Variables: Ccss.Math.Content.Hsa Ced.A.2

There are a total of 78 firefighters in a town. There are 4 fire departments in the town: North, South, East, and West. The North Department has 13 firefighters. The East Department has 43 firefighters. Let W represent the number of firefighters in the West Department and S represent the number of firefighters in the South Department. Which equation best illustrates this situation?

Possible Answers:

$\displaystyle 78=13+W+S$

$\displaystyle 13=78+43+W+S$

$\displaystyle 78=13+43+W+S$

$\displaystyle 43=78+13+W+S$

$\displaystyle 78=43+W+S$

Correct answer:

$\displaystyle 78=13+43+W+S$

Explanation:

To find the equation that represents this particular situation, the word problem will need to be translated into mathematical terms.

There are 78 firefighters in the town. The North Department has 13 firefighters. The East Department has 43 firefighters. Let W represent the number of firefighters from the West Department and S the number of firefighters in the South Department.

This question is talking about the total firefighters in one town and each section of the town has a different fire department. In mathematical terms this looks as follows:

From here, identify the values for the known variables.

$\\T=78 \\N=13 \\E=43$ $\displaystyle \\T=78 \\N=13 \\E=43$

Substitute the values into the equation.

$\displaystyle 78=13+43+W+S$

Report an Error

Example Question #3 : Equations With Two Or More Variables: Ccss.Math.Content.Hsa Ced.A.2

A candy shop contains a total of 30 items. There are 15 chocolates, 7 cookies, and T number of truffles. Write the equation that represents this situation.

Possible Answers:

30=7+T $\displaystyle 30=7+T$

$\displaystyle 15=30+7+T$

$\displaystyle 30=15+7+T$

30=15+T $\displaystyle 30=15+T$

$\displaystyle 7=15+30+T$

Correct answer:

$\displaystyle 30=15+7+T$

Explanation:

To find the equation that represents this particular situation, the word problem will need to be translated into mathematical terms.

A candy shop contains a total of 30 items. There are 15 chocolates, 7 cookies, and T number of truffles. In mathematical terms this looks as follows:

$\\\text{Total Candy Items}=\text{Chocolates + Cookies + Truffles} \\I=C+C_1+T$ $\displaystyle \\\text{Total Candy Items}=\text{Chocolates + Cookies + Truffles} \\I=C+C_1+T$

From here, identify the values for the known variables.

$\\I=30 \\C=15 \\C_1=7$ $\displaystyle \\I=30 \\C=15 \\C_1=7$

Substitute the values into the equation.

$\displaystyle 30=15+7+T$

Report an Error

Example Question #21 : Creating Equations✭

A coffee shop made 75 drinks in the first hour of operation, 20 mochas, 15 lattes, and C number of hot chocolates. Write an equation that represents this situation.

Possible Answers:

$\displaystyle 20=75+15+C$

$\displaystyle 75=20+15+C$

75=20+C $\displaystyle 75=20+C$

$\displaystyle 15=20+75+C$

75=15+C $\displaystyle 75=15+C$

Correct answer:

$\displaystyle 75=20+15+C$

Explanation:

To find the equation that represents this particular situation, the word problem will need to be translated into mathematical terms.

A coffee shop made 75 drinks in the first hour of operation, 20 mochas, 15 lattes, and C number of hot chocolates. In mathematical terms this looks as follows:

$\\\text{Total Drinks}=\text{Mochas + Latte + Hot Chocolate} \\T=M+L+C$ $\displaystyle \\\text{Total Drinks}=\text{Mochas + Latte + Hot Chocolate} \\T=M+L+C$

From here, identify the values for the known variables.

$\\T=75 \\M=20 \\L=15$ $\displaystyle \\T=75 \\M=20 \\L=15$

Substitute the values into the equation.

$\displaystyle 75=20+15+C$

Report an Error

Example Question #22 : Creating Equations✭

There are a total of 60 firefighters in a town. There are 4 fire departments in the town: North, South, East, and West. The North Department has 24 firefighters. The East Department has 9 firefighters. Let W represent the number of firefighters in the West Department and S represent the number of firefighters in the South Department. Which equation best illustrates this situation?

Possible Answers:

$\displaystyle 60=24+9+W+S$

$\displaystyle 9=24+60+W+S$

$\displaystyle 60=24+W+S$

$\displaystyle 60=9+W+S$

$\displaystyle 24=60+9+W+S$

Correct answer:

$\displaystyle 60=24+9+W+S$

Explanation:

To find the equation that represents this particular situation, the word problem will need to be translated into mathematical terms.

There are 60 firefighters in the town. The North Department has 24 firefighters. The East Department has 9 firefighters. Let W represent the number of firefighters from the West Department and S the number of firefighters in the South Department.

This question is talking about the total firefighters in one town and each section of the town has a different fire department. In mathematical terms this looks as follows:

From here, identify the values for the known variables.

$\\T=60 \\N=24 \\E=9$ $\displaystyle \\T=60 \\N=24 \\E=9$

Substitute the values into the equation.

$\displaystyle 60=24+9+W+S$

Report an Error

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All Common Core: High School - Algebra Resources

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Common Core: High School - Algebra : Equations with Two or More Variables: CCSS.Math.Content.HSA-CED.A.2

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

All Common Core: High School - Algebra Resources

Example Questions

Example Question #11 : Creating Equations✭

Example Question #12 : Creating Equations✭

Example Question #1 : Equations With Two Or More Variables: Ccss.Math.Content.Hsa Ced.A.2

Example Question #2 : Equations With Two Or More Variables: Ccss.Math.Content.Hsa Ced.A.2

Example Question #1 : Equations With Two Or More Variables: Ccss.Math.Content.Hsa Ced.A.2

Example Question #13 : Creating Equations✭

Example Question #2 : Equations With Two Or More Variables: Ccss.Math.Content.Hsa Ced.A.2

Example Question #3 : Equations With Two Or More Variables: Ccss.Math.Content.Hsa Ced.A.2

Example Question #21 : Creating Equations✭

Example Question #22 : Creating Equations✭

All Common Core: High School - Algebra Resources

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