Word Problem

Question

A stamp collection consists of 3 cent, 12 cent, and 15 cent stamps. The number of 3 cent stamps is five times the number of 12 cent stamps. The number of 15 cent stamps is four less than the number of the 12 cent stamps. The total value of the stamp collection is $3.18. Find the number of 15 cent stamps in the collection.

Answer 1

We know the LEAST about the number of 12 cent stamps. Read it again to see this, as we are told something about 3 cent and 15 cent stamps IN TERMS of the 12 cent stamps. THAT is where you assign the variable.

 

X is the number of 12 cent stamps.

 

The number of 3 cent stamps is 5X  <--- 5 times as many

 

The number of 15 cents stamps is X-4 <--- 4 less than

 

Their total value is $3.18 which in pennies is 318.

 

So in pennies, the equation becomes:

 

3 * # of 3-cent stamps + 12* # of 12-cent stamps + 15 * # of 15-cent stamps = 318

 

3 * (5X)                     + 12   X                            + 15(X-4)  =  318

 

15X + 12X + 15X - 60 = 318

 

42X - 60 = 318

 

42X = 318 + 60

 

42X = 378

 

x = 378/42 = 9

 

9    12-cent stamps

45   3 cents stamps

5    15-cent stamps

 

CHECK : 9x12 + 45x3 + 5 x 15 = 108 + 135 + 75 = 243 + 75 = 318