# 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 . . . . . . . $6 x$← number of 10ȼ stamps All the rest . . . . . . . $72 - 7 x$← 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 $- x \mathmr{and} - 6 x$Number of 20ȼ stamps . . . $72 - 7 x$........................... Now find a way to express the VALUE of each kind of stamp . $x$number of 5ȼ stamps @ 5ȼ ea. . . . . .$5 x$6$x$number of 10ȼ stamps @ 10ȼ ea. . . . .$60 x$(72 - 7x) 20ȼ stamps . . . @ 20ȼ ea . . $1440 - 140 x$........................ The values of all these stamps add up to 840ȼ [ value of 5ȼ ] "plus" [ value of 10ȼ ] "plus" [ . .value of 20ȼ ] = 840 [ . . . . $5 x$. . . .] . . + . . [ . . . .$60 x$. . . .] . . + . . [ (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 $- 75 x + 1440 = 840$2) Subtract $1440$from both sides to isolate the $- 75 x$term $- 75 x = - 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
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8 stamps @   5ȼ ea . . . . 40ȼ
48 stamps @ 10ȼ ea . . . 480ȼ
16 stamps @ 20ȼ ea. . . .320ȼ
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72 stamps . . . . . . . . . . . .840ȼ
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