Difference between revisions of "1996 AHSME Problems/Problem 7"
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Latest revision as of 14:07, 5 July 2013
Problem
A father takes his twins and a younger child out to dinner on the twins' birthday. The restaurant charges for the father and
for each year of a child's age, where age is defined as the age at the most recent birthday. If the bill is
, which of the following could be the age of the youngest child?
Solution
The bill for the three children is . Since the charge is
per year for the children, they must have
years among the three of them.
The twins must have an even number of years in total (presuming that they did not dine in the 17 minutes between the time when the first twin was born and the second twin was born). If we let the twins be years old, that leaves
years leftover for the youngest child. But if the twins are each
years old, then the youngest child could be
years old, which is choice
.
Of note, this is the only possibility for the ages of the children. If the twins were years old, the "younger" child would be
years old.
See also
1996 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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