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

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Question

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.

Answer

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,

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Question

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.

Answer

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,

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Question

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.

Answer

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,

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Question

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.

Answer

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,

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Question

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.

Answer

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,

Compare your answer with the correct one above

Question

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.

Answer

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,

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.

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

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Question

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.

Answer

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,

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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Question

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.

Answer

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,

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.

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

Compare your answer with the correct one above

Question

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.

Answer

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,

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.

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

Compare your answer with the correct one above

Question

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.

Answer

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,

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.

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

Compare your answer with the correct one above

Question

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?

Answer

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,

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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Question

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?

Answer

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,

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.

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

Compare your answer with the correct one above

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