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

21 shorts
21 shorts

10 shorts
10 shorts

30 shorts

Answer 1

To solve the problem, we can use the concept of ratios.

Let’s denote the number of shorts as \( S \) and the number of pants as \( P \).

According to the problem, the ratio of pants to shorts is given as 4:3, which can be expressed as:

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

From this ratio, we can express the number of pants in terms of the number of shorts:

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

We are also given that the total number of pants and shorts is 70:

\[
P + S = 70
\]

Now, we can substitute the expression we found for \( P \) into the total equation:

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

To combine the terms, we can express \( S \) as a fraction:

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

This simplifies to:

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

Now, we can solve for \( S \) by multiplying both sides by 3:

\[
7S = 210
\]

Now, divide both sides by 7:

\[
S = 30
\]

Thus, the number of shorts is \( \boxed{30} \).