Question

the ratio of small, medium, large shirts in a store is 3:x:2. if there are 30 small shirts and 20 large shirts, find the value of x and the number of medium shirts.

Answer 1

To solve for \( x \) and the number of medium shirts, we start with the given ratio of small, medium, and large shirts, which is represented as \( 3:x:2 \).

We know:

- The number of small shirts = 30 (let's denote this as \( S = 30 \))
- The number of large shirts = 20 (let's denote this as \( L = 20 \))

From the ratio \( 3:x:2 \), we can write relationships based on the given quantities.
Let the common multiple be \( k \). So we can express the quantities as:

- Number of small shirts (S) = \( 3k \)
- Number of medium shirts (M) = \( x = k \)
- Number of large shirts (L) = \( 2k \)

From the information provided:

1. For small shirts:
\[
3k = 30
\]
Solving for \( k \):
\[
k = \frac{30}{3} = 10
\]

2. For large shirts:
\[
2k = 20
\]
Since we've already calculated \( k \) to be 10, we can check:
\[
2 \times 10 = 20 \quad \text{(This is correct)}
\]

3. Now we find the number of medium shirts:
\[
x = k = 10
\]

Thus, the value of \( x \) is 10, and the number of medium shirts is also 10.

**Summary:**
- \( x = 10 \)
- Number of medium shirts = 10