SOLUTION: Lucy has 11 more dimes than pennies. She has $10.12 total. How many of each type of coin does she have?

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Question 1166932: Lucy has 11 more dimes than pennies. She has $10.12 total. How many of each type of coin does she have?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
system%28d-p=11%2C10d%2Bp=1012%29

ADD corresponding members.
11d=1023
highlight%28d=93%29---------------dimes

therefore highlight%2882%29-------------pennies

Answer by greenestamps(13334) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor has shown one formal algebraic solution.

I personally prefer to set up problems using a single variable if it is easy to do so.

Let x be the number of pennies; the number of dimes is then x+11.

Now we have a single equation to solve, instead of a system of two equations.

1%28x%29%2B10%28x%2B11%29+=+1012
x%2B10x%2B110+=+1012
11x+=+902
x+=+902%2F11+=+82

ANSWER: x = 82 pennies and x+11 = 93 dimes

If your mental arithmetic is good, you can get the answer informally, using virtually the same calculations as above.

(1) Count the "extra" 11 dimes, with a total value of 110 cents.
(2) the remaining amount, 1012-110 = 902 cents, is made up of equal numbers of pennies and dimes.
(3) 1 penny and 1 dime together have a value of 11 cents.
(4) The number of groups at 11 cents each needed to make the remaining 902 cents is 902/11 = 82.
(5) So there are 82 pennies and 82+11=93 dimes.