SOLUTION: 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 with a total value of $8.40. How many o

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Question 1101101: 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 with a total value of $8.40. How many of each stamp does he have?
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
Bruce has

(x of 5-cent stumps) + (6x 10-cent stamps) + (y 20-cent stumps)


Hence, you have these two equations:

(1)  x  + 6x      +    y =  72           (counting stamps)
(2)  5x + 10*(6x) + 20*y = 840  cents    (counting stamps' values) 


Simplify the equations

(1)   7x +   y =  72,
(2)  65x + 20y = 840.


From (1), express  y = 72-7x  and substitute it into eq(2). You will get

65x + 20*(72-7x) = 840  ====>

65x + 1440 - 140x = 840  ====>

-75x = 840 - 1440 = -600  ====>  x = %28-600%29%2F%28-75%29 = 8.


So, Bruce has  8  5-cent stamps;  8*6 = 48  10-cent stamps  and  72 - (8+48) = 16    20-cent stamps.


Answer.  Bruce has  8  5-cent stamps;  48  10-cent stamps  and  16  20-cent stamps.


Check.  5*8 + 10*48 + 20*16 = 840.  ! Correct !