SOLUTION: Joe has a collection of nickels and dimes tha is worth$5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Joe has a collection of nickels and dimes tha is worth$5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.      Log On


   

Question 149206: Joe has a collection of nickels and dimes tha is worth$5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45. How may dimes does he have? Please show all work...
So far all I can come up with is x =dimes, y= nickels.
x(2), y+8 =$10.45
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Hey, you already submitted this...
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Here's your solution:
Let n = number of nickels
and d = number of dimes
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Because we have two unknowns we need two equations:
From: "Joe has a collection of nickels and dimes that is worth $5.65." we get
.05n + .10d = 5.65 (equation 1)
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From: "If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45." we get:
.05(n+8) + .10(2d) = 10.45
.05n + .40 + .20d = 10.45
.05n + .20d = 10.05 (equation 2)
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n = 25 (nickels)
d = 44 (dimes)
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Below shows the details:
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 0.1*d to the right, we get:
0.05%2An+=+5.65+-+0.1%2Ad, or n+=+5.65%2F0.05+-+0.1%2Ad%2F0.05. Substitute that
into another equation:
0.05%2A%285.65%2F0.05+-+0.1%2Ad%2F0.05%29+%2B+0.2%5Cd+=+10.05 and simplify: So, we know that d=44. Since n+=+5.65%2F0.05+-+0.1%2Ad%2F0.05, n=25.

Answer: system%28+n=25%2C+d=44+%29.

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