Question

Chet has some 23 cent, 32 cent and 37 cent stamps. Their total value is $9.90. There are twice as many 32s as 23s, and five more 37s than there are 32s. How many stamps does Chet have ? Total # of stamps:___________

Answer 1

5 of 23 cents

10 of 32 cents

15 of 37 cents

In total that is 30 stamps.

Explanation:

This is going to be long, so bear with me.

0.23x + 0.32y +0.37z = 9.90

Here we define our variables.

Because we know that there is twice as much 32 cent stamps compared to 23 cents, we know: y =2x

So we can change that in the equation.

0.23x + 0.32(2x) + 0.37z = 9.90

0.23x + 0.64x + 0.37z = 9.90

We also know that there are 5 more 37 cent stamps than 32 cents.

So we can change all instances of z to 2x+5

0.23x + 0.64x + 0.37z(2x+5) = 9.90

0.23x +0.64x +0.74x +1.85 =9.90

Algebra:

0.23x +0.64x +0.74x = 9.90 -1.85

1.61x = 8.05

x = 5

From here we can just substitute it out and we find our values.

x = 5

y = 5 * 2

z = (5*2) +5