Problem 25 · 2011 Math Kangaroo
Stretch
Algebra & Patterns
substitution
An airline does not charge for luggage below a certain weight; for each additional kg there is a charge. Mr. and Mrs. Raiss had 60 kg of luggage and paid 3 €. Mr. Wander also had 60 kg of luggage but had to pay 10.50 €. How many kg of luggage per passenger were carried free?
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Answer: D — 25
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Hint 1 of 2
Mr. and Mrs. Raiss are two passengers; Mr. Wander is one — they share the same free allowance and rate.
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Hint 2 of 2
Set up the two charge equations and divide them to remove the rate.
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Approach: two charge equations, eliminate the per-kg rate by dividing
- Let f be the free kg per passenger and c the rate. Raiss: c(60 − 2f) = 3; Wander: c(60 − f) = 10.5.
- Dividing: (60 − f)/(60 − 2f) = 3.5, so 60 − f = 210 − 7f, giving 6f = 150.
- Thus f = 25 kg free per passenger.
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