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Common Core: High School - Algebra : High School: Algebra

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 #431 : High School: Algebra

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:

60=24+W+S

60=24+9+W+S

24=60+9+W+S

60=9+W+S

9=24+60+W+S

Correct answer:

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:

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

From here, identify the values for the known variables.

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

Substitute the values into the equation.

60=24+9+W+S

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Example Question #432 : High School: Algebra

A candy shop contains a total of 70 items. There are 45 chocolates, 7 cookies, and T number of truffles. Write the equation that represents this situation.

Possible Answers:

45=70+7+T

70=7+T

70=45+T

70=45+7+T

7=45+70+T

Correct answer:

70=45+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 70 items. There are 45 chocolates, 7 cookies, and T number of truffles. In mathematical terms this looks as follows:

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

From here, identify the values for the known variables.

$\\I=70 \\C=45 \\C_1=7$

Substitute the values into the equation.

70=45+7+T

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Example Question #433 : High School: Algebra

A coffee shop made 225 drinks in the first hour of operation, 80 mochas, 25 lattes, and C number of hot chocolates. Write an equation that represents this situation.

Possible Answers:

225=80+25+C

225=80+C

225=25+C

80=225+25+C

25=80+225+C

Correct answer:

225=80+25+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 225 drinks in the first hour of operation, 80 mochas, 25 lattes, and C number of hot chocolates. In mathematical terms this looks as follows:

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

From here, identify the values for the known variables.

$\\T=225 \\M=80 \\L=25$

Substitute the values into the equation.

225=80+25+C

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

There are 8 apples in a small fruit basket and 14 apples in a large fruit basket. If Sally buys a total of 5 fruit baskets that have a combined total of 58 apples, write an equation that represents the total number of apples that Sally has.

Possible Answers:

8s+14l=58

8s+58l=14

8s+5l=58

14s+8l=58

2s+4l=58

Correct answer:

8s+14l=58

Explanation:

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

$\\\text{small fruit basket}=8\text{ apples} \\\text{large fruit basket}=14\text{ apples}$

Now write the equation in words.

$\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=58\text{ apples}$

Let

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

therefore the equation becomes,

8s+14l=58

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Example Question #22 : Creating Equations✭

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 an equation that represents the total number of apples that Sally has.

Possible Answers:

34s+10l=6

6s+34l=10

6s+10l=32

6s+10l=34

8s+10l=34

Correct answer:

6s+10l=34

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

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Example Question #23 : Creating Equations✭

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 an equation that represents the total number of apples that Sally has.

Possible Answers:

5s+7l=3

7s+3l=31

3s+7l=31

3s+7l=5

3s+5l=31

Correct answer:

3s+7l=31

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

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Example Question #24 : Creating Equations✭

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 an equation that represents the total number of apples that Sally has.

Possible Answers:

10s+40l=5

5s+40l=10

5s+1l=40

10l=45

5s+10l=40

Correct answer:

5s+10l=40

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

Report an Error

Example Question #23 : Creating Equations✭

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 an equation that represents the total number of apples that Sally has.

Possible Answers:

15s+2l=95

15s+20l=95

95s+20l=5

5s+20l=95

95s+20l=15

Correct answer:

15s+20l=95

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

Report an Error

Example Question #24 : Creating Equations✭

There are 8 apples in a small fruit basket and 14 apples in a large fruit basket. If Sally buys a total of 5 fruit baskets that have a combined total of 58 apples, write the system of equation that represents the Sally situation.

Possible Answers:

$\\3s+2l=5 \\s+l=58$

$\\8s+14l=5 \\s+l=58$

$\\s+4l=5 \\8s+14l=58$

$\\8s+14l=58 \\s+l=5$

$\\8s+14l=58 \\5l=5$

Correct answer:

$\\8s+14l=58 \\s+l=5$

Explanation:

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

$\\\text{small fruit basket}=8\text{ apples} \\\text{large fruit basket}=14\text{ apples}$

Now write the equation in words.

$\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=58\text{ apples}$

Let

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

therefore the equation becomes,

8s+14l=58

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.

$\\8s+14l=58 \\s+l=5$

Report an Error

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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All Common Core: High School - Algebra Resources

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Common Core: High School - Algebra : High School: Algebra

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

All Common Core: High School - Algebra Resources

Example Questions

Example Question #431 : High School: Algebra

Example Question #432 : High School: Algebra

Example Question #433 : High School: Algebra

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

Example Question #22 : Creating Equations✭

Example Question #23 : Creating Equations✭

Example Question #24 : Creating Equations✭

Example Question #23 : Creating Equations✭

Example Question #24 : Creating Equations✭

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

All Common Core: High School - Algebra Resources

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