Brain Teasers
One Apple, Two Bananas, and One Orange
At a grocery store, apples cost "a" dollars each, bananas cost "b" dollars each, and oranges cost "o" dollars each, where "a", "b", and "o" are positive integers. Al bought "b" apples, "b" bananas, and "a"+"b" oranges, and paid 35 dollars. Ben bought one apple, two bananas, and one orange. How much money did Ben pay?
Answer
Ben paid 12 dollars.From Al's purchase, we know that:
b*a + b*b + (a+b)*o = 35
b*(a+b) + (a+b)*o = 35
(a+b)*(b+o) = 35
Since a, b, and o are positive integers, a+b and b+o are both integers greater than 2. The only pair of integers greater than 2 that multiplies to get 35 is 5 and 7, which means that a+b and b+o are 5 and 7, in some order.
Now we look at Ben's purchase. If p is the amount that Ben paid, then:
a + 2b + o = p
a + b+b + o = p
(a+b) + (b+o) = p
5+7 = p
12 = p
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