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Question

An illustration shows a set of three adjacent boxes labeled as Shorts. Another set of four adjacent rectangles is labeled as Pants and is placed below Shorts. All rectangles have the same dimensions. A bracket on the right side encompasses both sets and points to the number 70.

A clothing store has pants and shorts for sale in a ratio of 4:3 . If there are a total of 70 pants and shorts available for sale, how many of those are shorts?

(1 point)
Responses

40 shorts
40 shorts

10 shorts
10 shorts

21 shorts
21 shorts

30 shorts
30 shorts
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Answer 1

To solve the problem, we can use the ratio of pants to shorts and the total number available.

The ratio of pants to shorts is 4:3. This means for every 4 pants, there are 3 shorts.

Let's denote the number of pants as \( P \) and the number of shorts as \( S \). According to the ratio:

\[ \frac{P}{S} = \frac{4}{3} \]

This can be rewritten as:

\[ P = \frac{4}{3}S \]

We also know from the problem statement that the total number of pants and shorts is 70:

\[ P + S = 70 \]

Now we can substitute \( P \) in the total equation:

\[ \frac{4}{3}S + S = 70 \]

To combine the terms, convert \( S \) into a fraction:

\[ \frac{4}{3}S + \frac{3}{3}S = 70 \]

Which simplifies to:

\[ \frac{7}{3}S = 70 \]

Now, to solve for \( S \), multiply both sides by 3:

\[ 7S = 210 \]

Now, divide by 7:

\[ S = 30 \]

Thus, the number of shorts is \( S = 30 \).

So the answer is:

30 shorts