Problem 24 · 2021 Math Kangaroo
Stretch
Logic & Word Problems
casework
An apple and an orange weigh as much as a pear and a peach. An apple and a pear weigh less than an orange and a peach, and a pear and an orange weigh less than an apple and a peach. Which of the pieces of fruit is the heaviest?
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Answer: C — peach
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Hint 1 of 2
Turn each sentence into an inequality between sums of two fruits.
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Hint 2 of 2
Combine the inequalities to rank the fruits and spot the heaviest.
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Approach: combine the weight inequalities
- The balance apple + orange = pear + peach rearranges to peach = apple + (orange − pear).
- The two 'weigh less' facts force pear to be lighter than both apple and orange, so orange − pear is positive.
- Then peach = apple + (a positive amount) beats apple, and likewise peach beats orange, so the heaviest is peach.
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