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?

Answer 1

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

1. For Manny:

   • Pounds of red apples = 4
   • Pounds of green apples = 5
   • Ratio of red apples to green apples = \( \frac{4}{5} \)

2. For Vince:

   • Pounds of red apples = 3
   • Pounds of green apples = 6
   • Ratio of red apples to green apples = \( \frac{3}{6} \)
   • Simplifying \( \frac{3}{6} = \frac{1}{2} \)

Now we compare the two ratios:

• Manny's ratio of red to green apples is \( \frac{4}{5} \).
• Vince's ratio of red to green apples is \( \frac{1}{2} \).

To see if \( \frac{4}{5} \) is equal to \( \frac{1}{2} \), we'll convert both ratios to decimal form or cross-multiply.

Converting to decimal:

• \( \frac{4}{5} = 0.8 \)
• \( \frac{1}{2} = 0.5 \)

Since \( 0.8 \) is not equal to \( 0.5 \), the ratios are different.

Alternatively, cross-multiplying:

• For \( \frac{4}{5} = \frac{1}{2} \): cross-multiply to get \( 4 \times 2 = 8 \) and \( 1 \times 5 = 5 \).
• Since \( 8 \neq 5 \), they are not equal.

Thus, Manny and Vince did not pick the same ratio of red apples to green apples.