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Boris is ordering supplies for his company. He ordered $20$ boxes of pencils and $32$ boxes of pens. What is the ratio of boxes of pens ordered to boxes of pencils ordered?

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Solve proportions: word problems

Full solution

Q. Boris is ordering supplies for his company. He ordered

20

boxes of pencils and

32

boxes of pens. What is the ratio of boxes of pens ordered to boxes of pencils ordered?

Identify Quantities: Identify the quantities to be compared for the ratio. $\newline$ Boris ordered $20$ boxes of pencils and $32$ boxes of pens. We need to find the ratio of the number of boxes of pens to the number of boxes of pencils.
Calculate Ratio: Calculate the ratio. $\newline$ The ratio of boxes of pens to boxes of pencils is given by dividing the number of boxes of pens by the number of boxes of pencils. $\newline$ Ratio = $\frac{\text{Number of boxes of pens}}{\text{Number of boxes of pencils}}$ $\newline$ Ratio = $\frac{32}{20}$
Simplify Ratio: Simplify the ratio. $\newline$ To simplify the ratio, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of $32$ and $20$ is $4$ . $\newline$ Simplified Ratio = $(32 \div 4) / (20 \div 4)$ $\newline$ Simplified Ratio = $8 / 5$
Write Final Answer: Write the final answer. $\newline$ The simplified ratio of boxes of pens to boxes of pencils ordered by Boris is $8$ to $5$ .

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