Mr. Akika has 37 23​-cent and 28​-cent stamps all told. The stamps are worth ​$9.61. How many of each kind of stamp does he​ have?

Answer 1

Let c = cheaper stamps and e = more expensive stamps.

Here's what we know:

c + e = 37 (Mr. Akika has 37 stamps of a cheaper and more expensive stamp price in total)

.23c + .28e = 9.61 (all together, the stamps are worth $9.61)

The best way to solve this would be to use substitution. We can do that by isolating a variable in the first equation. Let's do so by subtracting e from both sides:

c = -e + 37

Now that we have a value for a variable, let's plug it in:

.23(-e + 37) + .28e = 9.61

distribute:

-.23e + 8.51 + .28e = 9.61

Combine like terms:

.05e + 8.51 = 9.61

Subtract 8.51 from both sides:

.05e = 1.1

Divide both sides by 0.05:

e = 22

Now find the cheaper stamp quantity:

c = -22 + 37 = 15

Check:

15 * .23 + 22 * .28 = 9.61

3.45 + 6.16 = 9.61

9.61 = 9.61