SOLUTION: A phone bill of $32.50 was paid in fifty cent pieces and quarters. the number of fifty cent pieces exceeded the number of quarter by five. how many of each were there
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Question 1178433: A phone bill of $32.50 was paid in fifty cent pieces and quarters. the number of fifty cent pieces exceeded the number of quarter by five. how many of each were there Found 3 solutions by math_helper, greenestamps, ikleyn:Answer by math_helper(2461) (Show Source):
Let x = number of 50¢ pieces
then x-5 = number of 25¢ pieces
Expressing $32.50 in cents, we get:
50x + 25(x-5) = 3250
Solve for x:
x = 45 = number of 50¢ pieces
x-5 = 40 = number of 25¢ pieces
let x = # of quarters
then x+5 = # of half dollars
The total value is $32.50, or 3250 cents:
Solve using basic algebra; I leave that much to you.
An informal solution using logical reasoning and easy mental arithmetic can get you to the solution faster then the formal algebra, and using very nearly the same steps.
(1) Count the "extra" five half dollars first. That's $2.50, or 250 cents; and it leaves equal numbers of quarters and half dollars with a total value of $30, or 3000 cents.
(2) Consider groups of one quarter and one half dollar; the value of each group is 75 cents.
(3) To make the remaining 3000 cents, the number of those groups needs to be 3000/75 = 40.
(4) So there are 40 quarters and 40+5=45 half dollars.
Of course the answer you got using formal algebra should be the same.
x = # of quarters
(x+5) = # of 50-cent coins.
The total money equation
25x + 50(x+5) = 3250 cents.
From the equation
x = = 40.
ANSWER. 40 quarters and 45 50-cent coins.
CHECK. 40*25 + 45*50 = 3250 cents. ! Correct !
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