SOLUTION: Joe has a collection of nickels and dimes that 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 $1

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Question 278824: Joe has a collection of nickels and dimes that 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 many dimes does he have?
Answer by Stitch(470) About Me  (Show Source):
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Set-Up
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Let A = Number of Nickels
Let b = Number of Dimes
Equation 1: A%2A0.05+%2B+B%2A0.1+=+5.65
Equation 2: %28A+%2B+8%29%2A0.05+%2B+2%2AB%2A0.1+=+10.45
Solution:
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You can divide every term in equation 1 by .05
Equation 1: A%2A0.05+%2B+B%2A0.1+=+5.65
A+%2B+2B+=+113 Subtract 2B from both sides
A+=+113+-+2B
Now we can plug (113 - 2B) into equation 2 for A
Equation 2: %28A+%2B+8%29%2A0.05+%2B+2%2AB%2A0.1+=+10.45
%28%28113+-+2B%29+%2B+8%29%2A0.05+%2B+2%2AB%2A0.1+=+10.45 Simplify
%28121+-+2B%29%2A0.05+%2B+B%2A0.2+=+10.45 Simplify
6.05+-+0.1%2AB+%2B+0.2%2AB+=+10.45 Simplify
6.05+%2B+0.1B+=+10.45 Subtract 6.05 from both sides
0.1B+=+4.40 Divide both sides by 0.1
highlight%28B+=+44%29
Now plug 44 into the modified equation 1 for B
A+=+113+-+2B
A+=+113+-+2%2A%2844%29
A+=+113+-+88
highlight%28A+=+25%29