by Bill Graham
Call the number of 33-cent stamps in the right pocket R33. Use
similar labels for the other stamps (R22, L33,
L22).
The value of the stamps in each pocket is the same.
33R33 + 22R22 = 33L33 + 22L22
The right pocket contains equal numbers of each type of stamp.
R33 = R22
The values of each stamp type in the left pocket are equal
33L33 = 22L22
You've got three equations in four variables and cannot simply solve.
You have two additional clues. First, the numbers must be integers;
you don't have any pieces of stamps. Second, the total value of the stamps
cannot exceed the money Humphrey spent, $20.
Substitute the second two equations into the first.
55R33 = 66L33
5R33 = 6L33
The values of R33 and L33 must be the same integer multiple of
6 and 5 respectively. You can readily see that only small multiples will keep
the total under $20. You could simply try them.
Note however, from the above equations,
R22 = R33 and L22 = 1.5L33
Therefore, L33 must be even. The integer multiple must be at least
two. If you use four, then you exceed the $20 limit.
R33 = 12, L33 = 10 => R22 = 12, L22 =
15
Summarizing:
Right pocket: 12(33) = $3.96, 12(22) = $2.64
Left pocket: 10(33) = $3.30, 15(22) = $3.30
Total = $13.20 on stamps leaving $6.80 for snacks.
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Vol 1, No 9 Answers
