SOLUTION: A student makes a $10.50 purchase at the bookstore with a $20 bill. The store has no bills and gives a change in quarters and 50 Cent pieces. There are 30 coins and all. How many o

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Question 1196792: A student makes a $10.50 purchase at the bookstore with a $20 bill. The store has no bills and gives a change in quarters and 50 Cent pieces. There are 30 coins and all. How many of each kind are there?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.

x = number of 50-cent pieces

(30-x) = the number of quarters.


Write the total money equation

    50x + 25*(30-x) = 950  cents  (the total change)


Simplify and find x

    50x + 750 - 25x = 950

       25x          = 950 - 750

       25x          =    200

         x          =    200/25 = 8.


ANSWER.  8 50-cent pieces and 30-8 =22 quarters.


CHECK.  8*50 + 22*25 = 950 cents,  total change.   ! Correct !

Solved.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If a formal algebraic solution is needed, use one like that provided in the response from the other tutor.

But this kind of relatively easy problem can provide good problem-solving practice and good mental exercise by solving it using logical reasoning and basic arithmetic.

(1) The required change is $9.50.
(2) If all 30 coins were quarters, that would be only $7.50, which is $2.00 short of the required total.
(3) Since each half dollar is worth $0.25 more than each quarter, the number of half dollars needed to make the addition $2.00 is 200/25 = 8.

So there were 8 half dollars, which means 30-8 = 22 quarters.

ANSWER: 8 half dollars; 22 quarters

CHECK: 8(50)+22(25) = 400+550 = 950