Question

Are these ratios equivalent? 96 pink dresses for every 58 indigo dresses 48 pink dresses for every 29 indigo dresses

Answer 1

To determine if the ratios are equivalent, we need to compare the two ratios given:

1. The first ratio is 96 pink dresses to 58 indigo dresses.
2. The second ratio is 48 pink dresses to 29 indigo dresses.

We can express these ratios as fractions:

1. For the first ratio: \(\frac{96}{58}\)
2. For the second ratio: \(\frac{48}{29}\)

To check if the ratios are equivalent, we can cross-multiply:

- For \(\frac{96}{58}\) and \(\frac{48}{29}\), we can cross-multiply:
- \(96 \times 29\) and \(58 \times 48\)

Calculating these:

1. \(96 \times 29 = 2784\)
2. \(58 \times 48 = 2784\)

Since both products are equal (2784 = 2784), the ratios \(\frac{96}{58}\) and \(\frac{48}{29}\) are indeed equivalent.

So yes, the ratios are equivalent.