14 Denver, Engle and Fldo are all dogs who eat differing amounts of dop food. Benver gets \( \frac{B}{19} \) of the dog food. Engle and Fido share the rest of the food in the ratio \( 9: 5 \) What is Fido's share of the dog food? Show your answer as a percentage, rounded to the nearest percent if necessay
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Beyond the Answer
Let's break this down in a fun way! First, we need to calculate how much dog food Benver gets. His share is \( \frac{B}{19} \). This leaves Engle and Fido with the remaining food, which is: \[ B - \frac{B}{19} = \frac{19B - B}{19} = \frac{18B}{19} \] Now, Engle and Fido share this remaining food in a ratio of \( 9:5 \). This means that the total parts of the ratio is \( 9 + 5 = 14 \) parts. To find Fido’s share, he gets \( 5 \) out of \( 14 \) parts of the remaining dog food: \[ \text{Fido's share} = \frac{5}{14} \times \frac{18B}{19} \] Calculating that gives: \[ Fido's share = \frac{90B}{266} = \frac{45B}{133} \] Now, to find Fido's share as a percentage of the total dog food \( B \), we calculate: \[ \text{Percentage} = \left(\frac{45B/133}{B}\right) \times 100 = \left(\frac{45}{133}\right) \times 100 \approx 33.83\% \] Rounding to the nearest percent, Fido's share of the dog food is approximately **34%**. How pawsitively delightful! 🐾
