Questions: 8. Faye and Omar ate the same amount of a small quesadilla. Faye's quesadilla was cut into 4 pieces and Omar's was cut into 8 pieces. How many pieces might they each have eaten? Explain your reasoning.

Solution Steps

To determine how many pieces Faye and Omar each ate, we need to find a common fraction that represents the same amount of quesadilla for both. Since Faye's quesadilla was cut into 4 pieces and Omar's into 8 pieces, we can express the amount they ate as fractions of their respective quesadillas and find equivalent fractions.

Faye and Omar ate the same amount of a small quesadilla, with Faye's quesadilla cut into 4 pieces and Omar's into 8 pieces. We need to find the possible number of pieces they each might have eaten such that the amount consumed is equivalent.

Let \( F \) be the number of pieces Faye ate and \( O \) be the number of pieces Omar ate. The fractions representing the amounts they ate can be expressed as: \[ \text{Faye's fraction} = \frac{F}{4} \] \[ \text{Omar's fraction} = \frac{O}{8} \] We need to find values of \( F \) and \( O \) such that: \[ \frac{F}{4} = \frac{O}{8} \]

Cross-multiplying gives us: \[ 8F = 4O \implies 2F = O \] This means for every piece Faye eats, Omar eats twice that amount. We can now list the possible values for \( F \) and \( O \) based on the maximum pieces they can eat.

The possible combinations of pieces they might have eaten are:

• If \( F = 1 \), then \( O = 2 \)
• If \( F = 2 \), then \( O = 4 \)
• If \( F = 3 \), then \( O = 6 \)
• If \( F = 4 \), then \( O = 8 \)

Thus, the pairs \((F, O)\) are: \[ (1, 2), (2, 4), (3, 6), (4, 8) \]

Final Answer