Bruce collects stamps. He has six times as many 10-cent stamps as 5-cent stamps, and he has some 20-cent stamps as well. Bruce has 72 stamps which are worth $8.40. How many of each stamp does he have?

Use tables to answer this question.

1 Answer
Nov 11, 2017

He has
Eight 5ȼ stamps
Forty-eight 10ȼ stamps
Sixteen 20ȼ stamps

Explanation:

Problems like this have two kinds of data
1) The NUMBER of stamps
2) The monetary VALUE of the stamps
.................

First find a way to express the NUMBER of each kind of stamp
Let x = "the number of 5ȼ stamps"

5ȼ stamps . . . . . . . . . . . . . .x ← number of 5ȼ stamps
6 times as many . . . . . . . 6x ← number of 10ȼ stamps
All the rest . . . . . . . 72 - 7x ← number of 20ȼ stamps

Here is how to figure the number of 20ȼ stamps
The number of 20ȼ stamps is the number remaining out of a total of 72 after you subtract the number of 5ȼ stamps as well as the number of 10ȼ stamps
Number of 20ȼ stamps . . . 72  stamps - x and- 6x
Number of 20ȼ stamps . . . 72 - 7x
...........................

Now find a way to express the VALUE of each kind of stamp
. x number of   5ȼ stamps @  5ȼ ea. . . . . .5x
6x number of 10ȼ stamps @ 10ȼ ea. . . . .60x
(72 - 7x) 20ȼ stamps . . . @ 20ȼ ea . . 1440 - 140x
........................

The values of all these stamps add up to 840ȼ
[ value of 5ȼ ] "plus" [ value of 10ȼ ] "plus" [ . .value of 20ȼ ] = 840
[ . . . . 5x . . . .] . . + . . [ . . . .60x . . . .] . . + . . [ (1440 - 140x)] = 840

5x   +   60x   +   (1440 - 140x)   =   840

Solve for x, already defined as "the number of 5ȼ stamps"

1) Collect like terms
(5x + 60x - 140x)   + 1440 = 840
- 75x + 1440 = 840

2) Subtract 1440 from both sides to isolate the -75x term
- 75x = - 600

3) Divide both sides by - 75 to isolate x, already defined as
"the number of 5ȼ stamps"
x = 8 ← the number of 5ȼ stamps

The number of 10ȼ stamps is 6 times as many
48 ← the number of 10ȼ stamps

The number of 20ȼ stamps is "all the rest"
72 total minus (eight 5ȼ stamps)  and  minus (48 10ȼ stamps)
72 total - (56 other stamps)
16 ← the number of 20ȼ stamps
...................

Check
  8 stamps @   5ȼ ea . . . . 40ȼ
48 stamps @ 10ȼ ea . . . 480ȼ
16 stamps @ 20ȼ ea. . . .320ȼ
.........................................................
72 stamps . . . . . . . . . . . .840ȼ
Check!