To find out how many dresses are in Amina's wardrobe, we can follow these steps:
1. Identify the given ratio: We are given that the ratio of T-shirts to dresses is [tex]\( 7:6 \)[/tex]. This means for every 7 T-shirts, there are 6 dresses.
2. Identify the number of T-shirts: We know there are 28 T-shirts in her wardrobe.
3. Set up a proportion: Since the ratio of T-shirts to dresses is [tex]\( 7:6 \)[/tex], we can set up a proportion to find the number of dresses. Let's denote the number of dresses by [tex]\( D \)[/tex].
The proportion can be written as:
[tex]\[
\frac{\text{Number of T-shirts}}{\text{Number of dresses}} = \frac{7}{6}
\][/tex]
Substituting the number of T-shirts we have:
[tex]\[
\frac{28}{D} = \frac{7}{6}
\][/tex]
4. Solve for the number of dresses (D): Now we solve for [tex]\( D \)[/tex] by cross-multiplying:
[tex]\[
28 \times 6 = 7 \times D
\][/tex]
[tex]\[
168 = 7D
\][/tex]
5. Divide both sides by 7 to isolate [tex]\( D \)[/tex]:
[tex]\[
D = \frac{168}{7}
\][/tex]
[tex]\[
D = 24
\][/tex]
Thus, there are 24 dresses in Amina's wardrobe.
