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Common Core: High School - Algebra : System of Equations and Inequalities: CCSS.Math.Content.HSA-CED.A.3

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

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All Common Core: High School - Algebra Resources

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Example Questions

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 $\displaystyle s=2$

s=5 $\displaystyle s=5$

s=3 $\displaystyle s=3$

s=1 $\displaystyle s=1$

s=4 $\displaystyle s=4$

Correct answer:

s=2 $\displaystyle s=2$

Explanation:

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

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

Now write the equation in words.

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

Let

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

therefore the equation becomes,

$\displaystyle 5s+10l=40$

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

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

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

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

Now, solve the second equation for $\displaystyle s$ .

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

Substitute this into the first equation.

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

Now substitute this value into the second equation to solve for $\displaystyle s$ .

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

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Example Question #12 : 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 large baskets does Sally have?

Possible Answers:

l=3 $\displaystyle l=3$

l=1 $\displaystyle l=1$

l=5 $\displaystyle l=5$

l=4 $\displaystyle l=4$

l=2 $\displaystyle l=2$

Correct answer:

l=3 $\displaystyle l=3$

Explanation:

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

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

Now write the equation in words.

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

Let

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

therefore the equation becomes,

$\displaystyle 5s+10l=40$

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

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

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

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

Now, solve the second equation for $\displaystyle s$ .

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

Substitute this into the first equation.

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

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Common Core: High School - Algebra : System of Equations and Inequalities: CCSS.Math.Content.HSA-CED.A.3

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

All Common Core: High School - Algebra Resources

Example Questions

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

Example Question #12 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

All Common Core: High School - Algebra Resources

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