Question 434946: Bertha has 33 coins in her pocket totaling $5.25. If she only has nickles and quarters, how many of each type of coin does she have
Found 4 solutions by mananth, ikleyn, josgarithmetic, greenestamps:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! nickels x Numbers
quarters ------------ y Numbers
x + 1 y = 33 .............1
x + 25 y = 525 .............2
multiply (1) by -25
x -25 y = -825
x 25 y = 525
x=-300
-20
= 15 = 15.00 nickels
x in (1)
x + y = 33
+ y = 33
y = 33 -15
y = 18
y = 18 = 18.00 quarters
Answer by ikleyn(53538)  (Show Source):
You can put this solution on YOUR website! .
Bertha has 33 coins in her pocket totaling $5.25. If she only has nickles and quarters,
how many of each type of coin does she have
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In the post by @mananth, his second equation in the 4th line is written incorrectly.
It makes all the subsequent solution defective.
So, I came to make the job accurately, in a way as it SHOULD be done.
In my solution, I will use one unknown and one equation, since it provides a shorter way.
Let x be the number of quarters.
Then the number of nickels is (33-x).
Write the total value equation
25x + 5*(33-x) = 525 cents.
Simplify and find x
25x + 165 - 5x = 525,
25x - 5x = 525 - 165,
20x = 360,
x = 360/20 = 18.
ANSWER. 18 quarters and 33-18 = 15 nickels.
CHECK for the total 25*18 + 5*15 = 525 cents, precisely as it is given in the problem.
Solved correctly.
Answer by josgarithmetic(39711)  (Show Source):
Answer by greenestamps(13276)  (Show Source):
You can put this solution on YOUR website!
The formal algebraic solutions shown by the other tutors are fine.
The problem can be solved informally using logical reasoning and mental arithmetic. If your mental arithmetic is good, this can be faster than using formal algebra. That can be helpful in some case, such as a timed competitive exam.
Solving problems informally can also provide excellent brain exercise.
Here is an informal solution to the problem.
(1) If all 33 coins were nickels, the total would be 33(5) = 165 cents, or $1.65. The actual total, $5.25, or 525 cents, is 525-165 = 360 cents more.
(2) Each quarter is worth 25-5 = 20 cents more than each nickel.
(3) The number of quarters needed to make the additional 360 cents is 360/20 = 18.
So there are 18 quarters and 33-18 = 15 nickels.
ANSWER: 18 quarters, 15 nickels
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