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A coin bank contains only nickels and dimes. The total value of the coins in the bank is $3.50.
If the nickels were dimes and the dimes were nickels, the total value of the coins would be $2.50.
Find the number of nickels in the bank.
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Let n be the number of nickels and d be the number of dimes.
Then
5n + 10d = 350 cents (1) ("The total value of the coins in the bank is $3.50. ")
10n + 5d = 250 cents (2) ("If the nickels were dimes and the dimes were nickels, the total value of the coins would be $2.50")
Cancel the factor 5 in both sides of both equations. You will get
n + 2d = 70 (3)
2n + d = 50 (4)
From (3), express n = 70-2d and substitute it into (4). You will get
2*(70-2d) + d = 50.
Simplify and solve for d:
140 - 4d + d = 50, or
-3d = 50 - 140 ---> -3d = -90 ---> d = 30.
Thus the number of dimes is 30.
Then the number of nickels, from (3), is n = 70-2d = 70 - 2*30 = 10.
Check it on your own.
Answer. 30 dimes and 10 nickels.
There is entire bunch of the lessons on coin problems
- Coin problems
- More Coin problems
- Solving coin problems without using equations
- Kevin and Randy Muise have a jar containing coins
- Typical coin problems from the archive
- More complicated coin problems
in this site.
Read them and become an expert in solution of coin problems.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
It contains many other solved word problems, as well as many other interesting and useful things.