SOLUTION: Roland has in his coin purse quarters and $1 coins. He has four more quarters than dollar coins and the total value of the coins is $4.75. How many of each does Roland have?

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Question 1116413: Roland has in his coin purse quarters and $1 coins. He has four more quarters than dollar coins and the total value of the coins is $4.75. How many of each does Roland have?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(1) set aside the 4 "extra" quarters. Now he has equal numbers of dollar coins and quarters, and the total value is $4.75-$1 = $3.75.

(2) one dollar coin and one quarter have a total value of $1.25. $3.75 is 3 times $1.25, so he has 3 dollar coins and 3 quarters.

(3) bring back the 4 "extra" quarters. He now has the full total of $4.75, consisting of 3 dollar coins and 3+4=7 quarters.

Algebraically....

let x = number of dollar coins
then x+4 = number of quarters

The total value of the coins is $4.75, or 475 cents:
x%28100%29%2B%28x%2B4%29%2825%29+=+475
100x%2B25x%2B100+=+475
125x+=+375
x+=+3

The number of dollar coins is x = 3; the number of quarters is x+4 = 3+4 = 7.

Note that the formal algebraic solution uses exactly the same arithmetic as the informal solution....