Question

Mr. Akika has 30 24-cent and 33-cent stamps all told. The stamps are worth $8.91. How many of each kind of stamp does he have?

Answer 1

• 24-cent: 11
• 33-cent: 19

Explanation:

I find it easiest to solve these using the variable to represent the number of the most-expensive item. Let x represent the number of 33-cent stamps. Then the total value (in cents) is ...

33x +24(30 -x) = 891

9x = 171 . . . . . . . . . . . . . subtract 24(30), collect terms

x = 19 . . . . . . . . . . . . divide by 9

30-x = 11 . . . . . . . find the number of 24-cent stamps

Mr. Akika had 11 24-cent stamps and 19 33-cent stamps.

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Additional comment

You seem to have several of these to solve. They all have a similar solution.

If we let x represent the number of higher-value items, N, the total number of items, V the total value, and v1 and v2 the individual values (v2 > v1), the equation is ...

v2(x) +v1(N -x) = V

x(v2 -v1) = V -v1·N

x = (V -v1·N)/(v2 -v1) . . . . generic solution

Using this formula in the problem here, we find ...

x = (891 -24(30))/(33 -24) = 171/9 = 19 . . . as above