SOLUTION: 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
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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
...
.02x = the value of all 2-cent stamps
.05y = the value of all 5-cent stamps
.07z = the value of all 7-cent stamps
...
Givens:
.02x + .05y + .07z = 1.44
x = y + 9
y = 2z
...
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.
...
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
...
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
...
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
...
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
...
So, according to our calculations, we have figured out there are:
21, 2-cent stamps
12, 5-cent stamps
6, 7-cent stamps
...
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
...
Problem solved. Good luck in the future...
...
cheers,
Lee
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