Question

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.

Answer 1

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`
6`x` 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!