If Alma wants to mail a package which requires $1.53 in postage, and has only 5-cent and 8-cent stamps, what is the smallest number of stamps she could use to total exactly $1.53?
(e) none of these
Let us say she uses x number of 5-cent and y number of 8-cent stamps.
`0.05x + 0.08y = 1.53`
`x + y = A ` (We want the minimum A)
`A = x + (1.53 – 0.05x) / 0.08 = (1.53 + 0.03x) / 0.08`
Put values for x (whole numbers) until we get a whole number to A
When x = 5 you get A=21.
This is the smallest number.
So the answer is (c)
As we need the least number of stamps to make $1.53 and we need to be exact, calculate how many 8c stamps come closest to the value
`19 times 8c = $1.52` so we can conclude that there are less that 19 stamps of 8c each. 8c stamps < 19
We also need to find a value of 8c stamps that leaves a multiple of 5c stamps so that we can be exact.
So if we use 16 8c stamps, having calculated that neither 18 nor 17 8c stamps leave a multiple of 5
`16 times 8c =$1.28` the balance remaining is 25c and
`5c times 5c = $0.25` 16 + 5 = 21. Option c) is correct.
Therefore c) is the correct answer. 21 stamps are the least number of stamps that can be used to total exactly $1.53