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20 coins, consisting of dimes and quarters.
if the values were switched, the difference would be 90 cents.
This is how i came up with my answer.
solving the system:
one equation describes the number of coins: x + y = 20
where x is the number of dimes and y is the number of quarters.
the other equation describes the amount of money:
(0.25x + 0.1y) - (0.1x + 0.25y) = 0.90
(0.25x + 0.1y) describes when the dimes are quarters and the quarters are dimes.
(0.1x + 0.25y) describes when the dimes and quarters are their original values.
The difference is supposed to be $0.90 or 90cents.
Therefore,
by the elimination method of solving a system of equations:
x + y = 20 #1
(0.25x + 0.1y) - (0.1x + 0.25y) = 0.9 #2
simplify #2 to become:
0.15x - 0.15y = 0.9 #3
x + y = 20 #1
0.15x - 0.15y = 0.9 #3
multiply #1 by 0.15:
0.15x + 0.15y = 3 #4
0.15x - 0.15y = 0.9 #3
add #4 and #3:
0.30x = 3.9
x = 13
therefore, the number of dimes that the man has is 13.
to find the number of quarters, x is evaluated in the 1st equation.
x + y = 20
13 + y = 20
y = 20 - 13
y = 7
This can be checked as follows.
13 dimes = 130 cents
7 quarters = 175 cents
total = 305 cents
13 quarters = 325 cents
7 dimes = 70 cents
total = 395 cents
The difference between the two is 90 cents.
Therefore, the man had 13 dimes and 7 quarters.
By the way, is this a question that you are doing in class, have the answer to and are seeing who can figure it out, or are you proposing it for another reason?
Addendum (by PatrickLMT): Actually, this question was featured in the February 26, 1974 comic strip "Peanuts." Peppermint Patty had this question in school and despaired of finding the answer.
Add your answer:
Earn +20 pts
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