Question

Joanie wants to mail a package that requires $1.30 in postage. If she has only 5-cent and 7-cent stamps, what is the smallest number of stamps she could use that would be totally exactly $1.30?

the smallest number of stamps is ____.

Answer 1

number of 5's --- x
number of 7's ---- y

5x + 7y = 130
5x = 130-7y
x = (130-7y)/5
x must be a whole number, so
130-7y must be divisible by 5, only if 7y is a multiple of 5

to get the least number of stamps we should use as many of the 7's (the y) as we can
if y = 15 , the last positive value making 130-6y divisible by 5
x = 5

<b>So she should use 5 fives and 15 sevens. total number = 20</b>

check:
5(5) + 15(7) = 130

other choices:
y = 10, x = 12 , total = $130, number of stamps = 22
y = 20, x = -2 , not possible