Question 260695
Barbara has 20 coins consisting of nickels and dimes. If the nickels were dimes
and the dimes were nickels, she would have 30¢ more than she has now. How
many dimes did she have to begin with?
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N = # of nickels
D = # of dimes
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5N + 10D = A  (some amount)
10N + 5D = A + 30
N + D = 20
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Sub for N or D, I'll do N
N = 20 - D
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5(20-D) + 10D = A
10(20-D) + 5D = A + 30
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+5D + 100 = A
-5D + 170 = A
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Since the equal A, the equal each other
5D + 100 = -5D + 170
D = 7
N = 13
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You can check it.
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Do it this way:
A change in the total of 30 means a change of 6 coins from nickels to dimes.
That makes the problem:
N + D = 20
N - D = 6
2N = 26
N = 13
D = 7