Steve has 54 stamps in his collection of 13 cent, 29 cent, and 45 cent stamps, totaling a value of $15.98. If the number of 13 cent stamps is doubled, the new total value of his stamp collection would be $17.80. Find the number of each type of stamp in his collection.

Number of 13 cents stamp = 14

Number of 29 cents stamp = 24

Number of 45 cents stamp = 16

Step-by-step explanation:

We are told he has 54 stamps in total.

These stamps are;13 cent, 29 cent, and 45 cent stamps.

Let's call number of 13 cent($0.13) stamp A

Call number of 29 cent($0.29) stamp B

Call number of 45 cent($0.45) stamp C

Thus;

A + B + C = 54

We are told the total value of the 3 stamps are $15.98.

Thus;

0.13A + 0.29B + 0.45C = $15.98 - - - (eq2)

Now we are told that if the number of 13 cent stamps is doubled, the new total value of his stamp collection would be $17.80.

Thus;

2(0.13A) + 0.29B + 0.45C = 17.8

0.26A + 0.29B + 0.45C = 17.8 - - - (eq 3)

Solving the 3 equations simultaneously, we have;

A = 14

B = 24

C = 16

We have;

Number of 13 cents stamp = 14

Number of 29 cents stamp = 24

Number of 45 cents stamp = 16