A woman bought some 13 cent stamps and some 8 cent stamps at the posg office. She spent exactly 1 dollar. How many of each stamp could she have bought?

Answer 1

number of 13 cent stamps --- x
numbr of 8 cent stamps -- y

13x + 8y = 100
both x and y have to be whole numbers
clearly 0 < x < 7
y = (100-13x)/8
furthermore, for 100-13x to be divisible by 8, it must be even, so x must be even
A quick check tells us that x = 4 is the only solution in our domain
if x = 4, y = 6
so 4 13's and 6 8's

check:
4(13) + 6(8) = 100