Question

Bianca has a stamp collection of 5 cent stamps and 7 cent stamps. She has 3 less 7 cent stamps as 5 cent stamps. If the collection has a face value of 87 cents, how many of each does she have?

She has ____ 5 cent stamps and ____ 7 cent stamps.

Answer 1

Number of 5 cent stamps = 9

Number of 7 cent stamps = 6

Explanation:

We are given that Bianca has a stamp collection of 5 cent stamps and 7 cent stamps in which there are 3 less 7 cent stamps as 5 cent stamps.

If the total face value of stamps is 87 cents, we are to find the number of stamps of each value.

Assuming
`t` to be the number of 5 cent stamps and
`s` to be the 7 cent stamps so we can write it as:

`0.05t+0.07s=0.87` --- (1)

`s=t-3` --- (2)

Substituting this value of
`s` from (2) in (1):

`0.05t+0.07(t-3)=0.87`

`0.05s+0.07t-0.21=0.87`

`0.12t=1.08`

`t=9`

Number of 5 cent stamps = 9

Number of 7 cent stamps = 9 - 3 = 6

Answer 2

She has 9 5 cent stamps and 6 7 cent stamps.

Explanation:

Let the number of five cent stamps be represented by F and the number of seven cent stamps be represented by S.

The difference between the number of five cent and seven cent stamps is 3

F-S=3

The sum of the collection from each type of stamp is 87 cents

5F+7S=87

Let us solve the equations simultaneously.

F-S=3

5F+7S=87

Using substitution method,

F= 3+S

5(3+S)+7S=87

15+5S+7S=87

12S=87-15

12S=72

S=6

F=3+S

=3+6=9

Therefore the number of five cent stamps is 9 and seven cent stamps is 6.