Willie has 14 coins of two types: dimes and qaurters. The overall value of the 14 coins is $2.30 How many of each does he have?

We have 14 coins, all dimes and quarters, with a total worth of $2.30, and we want to know the number of each type of coin.

Note that a dime is worth 10 cents, and a quarter is worth 25 cents.

Now let d be the number of dimes, and q the number of quarters.

Then we know d+q = 14 since there are 14 coins.

Also .1d+.25q=2.3 or 10d+25q=230 ==> 2d+5q=46

We have two equations with two unknowns -- this can be solved (assuming there is a solution) using guess and check, substitution, or linear combinations (often called the elimination method or the multiplication and addition method.)

d+q=14
2d+5q=46  Multiply equation 1 by 2 and subtract from equation 2:

3q=18 so q=6 and then d=8

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There are 8 dimes and 6 quarters

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Check: 8+6= 14 coins and .80+1.5=2.3 as required.