Question

Manny and his friend Vince go apple-picking every October. This year, Manny picked 4 pounds of red apples and 5 pounds of green apples. Vince picked 3 pounds of red apples and 6 pounds of green apples. Did Manny and Vince pick the same ratio of red apples to green apples?

Yes or No?

Answer 1

To determine if Manny and Vince picked the same ratio of red apples to green apples, we need to calculate the ratio for each of them.

For Manny:
- Red apples: 4 pounds
- Green apples: 5 pounds

The ratio of red apples to green apples for Manny is:
\[ \frac{\text{Red}}{\text{Green}} = \frac{4}{5} \]

For Vince:
- Red apples: 3 pounds
- Green apples: 6 pounds

The ratio of red apples to green apples for Vince is:
\[ \frac{\text{Red}}{\text{Green}} = \frac{3}{6} = \frac{1}{2} \]

Now we compare the two ratios:
- Manny's ratio is \( \frac{4}{5} \).
- Vince's ratio is \( \frac{1}{2} \).

To check if they are the same, we can cross-multiply:
\[ 4 \times 2 = 8 \]
\[ 5 \times 1 = 5 \]
Since \( 8 \neq 5 \), the ratios are not equal.

Therefore, the answer is **No**, Manny and Vince did not pick the same ratio of red apples to green apples.