Cent/Stamp Math Question, I'm having a big difficulty with this.

Question

The number of 25-cent stamps is 4 more than twice the number of 42-cent stamps. There is 3 times the number of 68-cent stamps as 25-cent stamps. If their total value is $34.16, how many stamps are there altogether?

Answer 1

Hi, there!

Okay, so let's set variables for the numbers of stamps.

Okay, so let's let:

X = the number of 42-cent stamps.

Y = the number of 25 cents stamps

Z = the number of 68 cent stamps

The number of 25 cent stamps is 4 more than twice the number of 42 cent stamps so:

Y = 2X + 4

There are 3 times the number of 68 cent stamps as 25 cent stamps so:

Z = 3Y = 3(2X + 4)

So now :

.42X + .25Y + .68Z = 34.16

Now we can substitute all the variables in terms of X from above:

.42X + .25(2X + 4) + .68(6X + 12) = 34.16

.42X + .50X + 1 + 4.08X + 8.16 = 34.16

5X + 9.16 = 34.16

5X = 25

X = 5

So, there are: 5 "42-cent stamps"

There are 2X + 4 = 14 "25- cent stamps"

There are 3 x 14 = 42 " 68- cent stamps"

Now, you can check your answer

5(.42) + 14(.25) + 42(.68)

= 2.10 + 3.50 + 28.56

= 34.16