SOLUTION: THER ARE 4 TIMES AS MANY NICKELS AS DIMES IN A COIN BANK. THE COINS HAVE A TOTAL VALUE OF 600 CENTS ($6.00). FIND THE NUMBER OF NICKELS.

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Question 112006This question is from textbook algebra 1
: THER ARE 4 TIMES AS MANY NICKELS AS DIMES IN A COIN BANK. THE COINS HAVE A TOTAL VALUE OF 600 CENTS ($6.00). FIND THE NUMBER OF NICKELS. This question is from textbook algebra 1

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Any set of coins has two characteristics, one is the total value of the coins, and the other is the number of coins. For example, if you have 10 nickels, the number of coins is 10 and the value is 50 cents. So this should give us a clue as to how to proceed.

Let's say the number of nickels is n and the number of dimes is d. The nickels are worth 5 * n cents, and the dimes are worth 10 * d cents. And the total value of all the coins is 600 cents, so we can write 5n%2B10d=600.

We also know that there are four times as many nickels as dimes. That means that 4 * d = n. We can substitute this fact into the value equation to give us an equation in a single variable that we can solve directly.

5%284d%29%2B10d=600

20d%2B10d=600

30d=600

d=20

n+=+4%2A20+=+80, so there are 80 nickels.

Last step -- VERY IMPORTANT: Check your answer.

5 * 80 = 400 and 10 * 20 = 200 and 400 plus 200 = 600, and finally 80 = 4 * 20. And the answer of 80 nickels satisfies all of the conditions of the problem.