Problema Solution
A student bought 23-cent, 41-cent, and 80-cent stamps with a total value of $31.50. If the number of 23-cent stamps is 2 more than the number of 41-cent stamps, and the number of 80-cent stamps is 5 more than one-half the number of 41-cent stamps, how many stamps of each denomination did the student obtain?
Answer provided by our tutors
let
x = the number of 23-cent stamps
y = the number of 41-cent stamps
z = the number of 80-cent stamps
A student bought 23-cent, 41-cent, and 80-cent stamps with a total value of $31.50 = 3150 cents
23x + 41y + 80z = 3150
the number of 23-cent stamps is 2 more than the number of 41-cent stamps
x = 2 + y
the number of 80-cent stamps is 5 more than one-half the number of 41-cent stamps
z = 5 + y/2
by solving the system of equations
23x + 41y + 80z = 3150
x = 2 + y
z = 5 + y/2
we find
x = 28 23-cent stamps
y = 26 41-cent stamps
z = 18 80-cent stamps
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