Question 1130095: Andy has 31 coins made up of quarters and half dollars. The total is $11.00. How many quarters does he have? Found 2 solutions by josgarithmetic, greenestamps:Answer by josgarithmetic(39630) (Show Source):
Let me start with the same equation as the other tutor but solve the equation a bit differently; then I will show you how the problem can be solved more quickly using an informal method, with exactly the same calculations, but without the formal algebra.
ANSWER: the number of quarters is q = 18.
Here is how you can solve the problem informally with logical reasoning, leading to exactly the same calculations. If the speed with which the problem is solved is important, and a formal algebraic solution is not required (as in a math competition), then this is a good method to use.
(1) If all 31 coins were half dollars, the total value would be $15.50; the actual value is $11.00, which is $4.50 less.
(2) Replacing a half dollar with a quarter keeps the total number of coins the same but reduces the total value by $0.25.
(3) The number of times needed to replace a half dollar with a quarter, to reduce the total by $4.50 to the required $11.00, is $4.50/$0.25 = 450/25 = 18.
ANSWER: There must be 18 quarters among the 31 coins.
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