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There are four more nickels than dimes in a piggy bank. The total amount of money is $2.45. How many of each type of coin is in the bank?

Mathematics
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you have 15 dimes and 19 nickles .. therefore you have 4 more nickles then dimes because 15 time 0.10 = 1.50 and 19 times 0.05 = 0.95 then you take 1.50 + 0.95 = 2.45
If you had only nickels you will have 49 coins. replacing two nickels by a dime keeps the amount same so 0 dimes + 49 nickels = 5 dimes + 39 nickels = 10 dimes + 29 nickels ... this should lead you to the answer
Let N = the number of nickels Let D = the number of dimes There will be two equations in two unknowns (N and D) to solve simultaneously. D + 4 = N 10D + 5N = 245 --> This is equivalent to .10D + .05N = 2.45 --------------- Solve by substitution. D = N - 4 10( N - 4) + 5N = 245 10N - 40 + 5N =245 15N - 40 = 245 15N = 285 N = 19 -----> 19 Nickels D = N - 4 D = 19 - 4 = 15 ------> 15 Dimes Check: 15 = 19 - 4 10 ( 15 ) + 5 ( 19 ) = 150 + 95 = 245 cents which is $2.45

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thanks Directrix, this is it, and it makes sense.
Glad to help.

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