SOLUTION: she has 1.10, she has three times as many 5-cents coins as 1 cent coins, and the number of 10 cents coins is two less than the number of 1 cent coins. how many 10 cents coins, 5 ce

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Question 1141370: she has 1.10, she has three times as many 5-cents coins as 1 cent coins, and the number of 10 cents coins is two less than the number of 1 cent coins. how many 10 cents coins, 5 cents coins, and 1 cent coins does she have?
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The information is given in such a way that the numbers of 5-cent and 10-cent coins are both defined in terms of the number of 1-cent coins. So choosing x to represent the number of 1-cent coins should make the problem easiest.

Let x = # of 1-cent coins
Then 3x = # of 5-cent coins
And x-2 = # of 10-cent coins

Now write and solve the equation that says the total value is $1.10, or 110 cents:



You can finish solving the problem from there....

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You can also solve the problem informally using logical reasoning.

(1) The total value of all the coins (110) is a multiple of 5; and the total value of all the 5- and 10-cent coins is a multiple of 5. That means the total value of the 1-cent coins must be a multiple of 5 -- i.e., the number of 1-cent coins is a multiple of 5.

(2) So the number of 1-cent coins is 5, or 10, or 15, ....

(3) But the number of 5-cent coins is 3 times the number of 1-cent coins. If the number of 1-cent coins were 10, the number of 5-cent coins would be 30; and 30 5-cent coins is more than the actual total value of all the coins.

(4) So the number of 1-cent coins HAS TO BE 5. Then the number of 5-cent coins is 3*5 = 15, and the number of 10-cent coins is 5-2 = 3.

CHECK: 3(10)+15(5)+5(1) = 30+75+5 = 110

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Knowing how to solve problems like this using formal algebra is of course useful... but it is excellent brain exercise to be able to solve them using logical reasoning.
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
COINS                      QUANTITY OF COINS
ten cent coins              p-2
five cent coins             3p
one cent coins               p
TOTAL cents                 110


Solve and find the other coin amounts.
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