To solve the problem, we need to determine how much of the hoagie Evan ate for lunch after he had already consumed some for dinner.
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Calculate what was left after dinner: Evan ate \(\frac{3}{8}\) of the hoagie for dinner, which means the amount left is: \[ 1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8}. \]
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Determine how much he ate for lunch: Next, Evan ate two-thirds of what was left for lunch. To find this, we can multiply the remaining part of the hoagie by \(\frac{2}{3}\): \[ \frac{2}{3} \times \frac{5}{8} = \frac{2 \times 5}{3 \times 8} = \frac{10}{24}. \] We can simplify \(\frac{10}{24}\): \[ \frac{10}{24} = \frac{5}{12}. \]
Thus, Evan ate \(\frac{5}{12}\) of the entire hoagie for lunch.
The correct process to use would be:
- First, calculate what was left after dinner (1 - \(\frac{3}{8}\)).
- Then, calculate two-thirds of the remaining amount.
The best response from the list of options provided is: \(\frac{5}{8} \times \frac{2}{3} = \frac{10}{24} = \frac{5}{12}\).
2 answers