Question

if 5 oz of a solution contains \\(4\frac{1}{2}\\) oz of water, how many oz of water are in 20 oz of solution?

Explanation:

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<reasoning>

Identify the given values and relationship

We are given a proportional relationship between the total volume of a solution and the volume of water it contains:

• Given solution volume: \(5\text{ oz}\)
• Given water volume: \(4\frac{1}{2}\text{ oz}\)
• Target solution volume: \(20\text{ oz}\)
• Target water volume: \(x\text{ oz}\)

Set up the proportion

Using Proportional Reasoning, we set up a ratio of water to total solution:
\[
\frac{\text{Water}}{\text{Solution}} = \frac{4\frac{1}{2}\text{ oz}}{5\text{ oz}} = \frac{x\text{ oz}}{20\text{ oz}}
\]

Solve for the unknown water volume

To find \(x\), we multiply both sides of the proportion by \(20\):
\[
x = 20 \times \frac{4\frac{1}{2}}{5}
\]
Simplify the fraction coefficient:
\[
\frac{20}{5} = 4
\]
Thus, the calculation reduces to:
\[
x = 4 \times 4\frac{1}{2}
\]

Perform mixed number multiplication

Using Mixed Number Multiplication, we convert the mixed number to an improper fraction:
\[
4\frac{1}{2} = \frac{9}{2}
\]
Now, multiply by \(4\):
\[
x = 4 \times \frac{9}{2} = \frac{36}{2} = 18\text{ oz}
\]
</reasoning>

<answer>
If 5 oz of a solution contains 4 1/2 oz of water, how many oz of water are in 20 oz of solution? <blank>18</blank>
</answer>

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Answer:

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<reasoning>

Identify the given values and relationship

We are given a proportional relationship between the total volume of a solution and the volume of water it contains:

• Given solution volume: \(5\text{ oz}\)
• Given water volume: \(4\frac{1}{2}\text{ oz}\)
• Target solution volume: \(20\text{ oz}\)
• Target water volume: \(x\text{ oz}\)

Set up the proportion

Using Proportional Reasoning, we set up a ratio of water to total solution:
\[
\frac{\text{Water}}{\text{Solution}} = \frac{4\frac{1}{2}\text{ oz}}{5\text{ oz}} = \frac{x\text{ oz}}{20\text{ oz}}
\]

Solve for the unknown water volume

To find \(x\), we multiply both sides of the proportion by \(20\):
\[
x = 20 \times \frac{4\frac{1}{2}}{5}
\]
Simplify the fraction coefficient:
\[
\frac{20}{5} = 4
\]
Thus, the calculation reduces to:
\[
x = 4 \times 4\frac{1}{2}
\]

Perform mixed number multiplication

Using Mixed Number Multiplication, we convert the mixed number to an improper fraction:
\[
4\frac{1}{2} = \frac{9}{2}
\]
Now, multiply by \(4\):
\[
x = 4 \times \frac{9}{2} = \frac{36}{2} = 18\text{ oz}
\]
</reasoning>

<answer>
If 5 oz of a solution contains 4 1/2 oz of water, how many oz of water are in 20 oz of solution? <blank>18</blank>
</answer>

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