Question

Jake has $7.13 worth of stamps on his desk. He has 1-cent stamps, 5-cent stamps, and 25-cent stamps. The number of 25-cent stamps is 6 less than twice the number of 1-cent stamps. The number of 5-cent stamps is twice the number of 25-cent stamps. How many of each kind of stamps were on Jake's desk?

Answer 1

Jake has 15 1-cent stamps, 24 25-cent stamps, and 48 5-cent stamps on his desk, which all together sum up to his $7.13 worth of stamps.

Step-by-step explanation:

Let us define the number of 1-cent stamps as x. According to the problem, the number of 25-cent stamps is 6 less than twice the number of 1-cent stamps, so we can express the number of 25-cent stamps as 2x - 6. The number of 5-cent stamps is twice the number of 25-cent stamps, which gives us 2(2x - 6). Now, we can set up an equation to represent the total value of the stamps, which is $7.13.

The equation will be:

1. (0.01 × x) + (0.05 × 2(2x - 6)) + (0.25 × (2x - 6)) = 7.13

Solving this equation:

1. 0.01x + 0.10(2x - 6) + 0.50x - 3 = 7.13
2. 0.01x + 0.2x - 0.6 + 0.50x - 3 = 7.13
3. 0.71x - 3.6 = 7.13
4. 0.71x = 7.13 + 3.6
5. 0.71x = 10.73
6. x = 10.73 / 0.71
7. x = 15

So Jake has 15 1-cent stamps. The number of 25-cent stamps is 2(15) - 6 = 24. The number of 5-cent stamps is twice the number of 25-cent stamps, which gives us 2 × 24 = 48.

Therefore, Jake has 15 1-cent stamps, 24 25-cent stamps, and 48 5-cent stamps on his desk.