Question

Kenji feeds his cats a mixture of wet and dry food at every meal. He mixes 5 spoonfuls of dry food and 10 spoonfuls of wet food for Tiger, his adult cat. He mixes a smaller meal with 3 spoonfuls of dry food and 5 spoonfuls of wet food for his kitten, Smokey. Do the two meals have the same ratio of dry food to wet food?

Answer 1

To determine if the two meals have the same ratio of dry food to wet food, we need to calculate the ratios for both Tiger's and Smokey's meals.

**For Tiger's meal:**
- Amount of dry food = 5 spoonfuls
- Amount of wet food = 10 spoonfuls

The ratio of dry food to wet food for Tiger is:
\[
\text{Ratio for Tiger} = \frac{\text{dry food}}{\text{wet food}} = \frac{5}{10} = \frac{1}{2}
\]

**For Smokey's meal:**
- Amount of dry food = 3 spoonfuls
- Amount of wet food = 5 spoonfuls

The ratio of dry food to wet food for Smokey is:
\[
\text{Ratio for Smokey} = \frac{\text{dry food}}{\text{wet food}} = \frac{3}{5}
\]

Now we compare the two ratios:
- Tiger's ratio = \(\frac{1}{2}\)
- Smokey's ratio = \(\frac{3}{5}\)

To see if these ratios are equal, we can express them with a common denominator or convert them to decimal:

1. Convert to decimal:
- \( \frac{1}{2} = 0.5 \)
- \( \frac{3}{5} = 0.6 \)

Since \(0.5 \neq 0.6\), the two ratios are not the same.

2. Another method is to cross multiply:
- For \(\frac{1}{2} = \frac{3}{5}\):
- Cross multiplying gives: \(1 \cdot 5 \neq 2 \cdot 3\) or \(5 \neq 6\).

Thus, both methods confirm that the ratios of dry food to wet food in Tiger's and Smokey's meals are different.

In conclusion, **the two meals do not have the same ratio of dry food to wet food**.