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Answer:
- A and B: 1/4x, x -3/4x
- A and C: 8/5x, x +3/5x
Step-by-step explanation:
The wording of these questions is ambiguous, and <em>should be avoided</em>. Statements describing amounts "more" (or "farther") or "less" usually are describing a quantity that is in the original measure.
For example, "2 kegs and 3 more" would generally be interpreted to mean 5 kegs.
An exception to this interpretation is usually intended when percentages are involved. "2 kegs and 50% more" would generally be interpreted to mean 3 kegs, the original 2 plus 50% of 2, or 1 more. This is most often seen in pricing, where percentages are used to express markups or discounts.
Here, the notion of (some amount) and (some fraction) more (or less) could mean that a fraction of the original unit is being added (or subtracted). Or, it could mean that a fraction of the original quantity is being added (or subtracted). That is, we could interpret "2 kegs and 1/2 more" to mean 2 1/2 kegs, or 2 +(1/2)(2) = 3 kegs. It is this ambiguity that is present in these questions.
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For these answers, we will (reluctantly) interpret the fraction to mean a fraction of the original <em>quantity</em>, not the original <em>unit</em>.
1. 3/4 of x fruit snacks will be 3/4x. When that amount is subtracted from x, we have ...
x - 3/4x = 1/4x
These expressions match the first and second choices, "A" and "B".
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2. 3/5 of x miles will be 3/5x miles. When that amount is added to x, we have ...
x + 3/5x = 8/5x
These expressions match the first and third choices, "A" and "C".
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Please be aware that the alternate interpretation is completely legitimate. More context is needed to resolve the ambiguity. (That context may be supplied by examples or rules given in your curriculum materials.) That is, appropriate answers might also be ...
1. x -3/4 (one choice only) -- assumes 3/4 of a fruit snack
2. x +3/5, 3/5 +x (two choices) -- assumes 3/5 of a mile
