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Question 535489: A collection of stamps consist of2,5,and 7 cent stamps. There are nine more two cent stamps then 5 cent stamps and twice as many 7 cent stamps as 5 cent stamps. The total value of he stamps is $1.44. Find the number of each type of stamp in the collection
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! Let x = # 2-cent stamps
Let y = # 5-cent stamps
Let z = # 7-cent stamps
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.02x = the value of all 2-cent stamps
.05y = the value of all 5-cent stamps
.07z = the value of all 7-cent stamps
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Givens:
.02x + .05y + .07z = 1.44
x = y + 9
y = 2z
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We have 3 equations and 3 unknowns. This is easily solved by finding a way to reduce the number of unknowns till eventually we have one equation in one unknown, which we can solve for, then substituting that answer back into the other equations.
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Let's express x and z in terms of y, then we can plug these into the 1st equation. We already have x in terms of y, so that is a direct substitution. In the last equation, y = 2z can be rewritten:
z = .5y
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Now go back to the first equation substituting x and z in terms of y:
.02x + .05y + .07z = 1.44
.02(y + 9) + .05y + .07(.5y) = 1.44
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combine like terms and simplify:
.02y + .18 + .05y + .035y = 1.44
.105y + .18 = 1.44
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subtract .18 from both sides:
.105y + .18 - .18 = 1.44 - .18
.105y = 1.26
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divide both sides by .105:
y = 1.26/.105
y = 12
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Now we know we have 12, 5-cent stamps. If we plug that back into our equation linking x and y, we can figure out how many x (2-cent) stamps there are:
x = y + 9
x = 12 + 9
x = 21
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Likewise, since we stated z in terms of y, we can figure out how many 7-cent stamps there are:
z = .5y
z = .5(12)
z = 6
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So, according to our calculations, we have figured out there are:
21, 2-cent stamps
12, 5-cent stamps
6, 7-cent stamps
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Now we need to check our work. Go back to our original equation to see of the numbers add up:
.02(21) + .05(12) + .07(6) = 1.44
.42 + .60 + .42 = 1.44
1.44 = 1.44 checks
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Problem solved. Good luck in the future...
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cheers,
Lee
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