SOLUTION: A collection of nickels, dimes, and quarters is retrieved from a vending machine. There are three times as many nickels as dimes, and there are ten more quarters than dimes. If t

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Question 1200567: A collection of nickels, dimes, and quarters is retrieved from a vending machine. There are three times as many nickels as dimes, and there are ten more quarters than dimes. If the total value of the coins is $40.00 then find the number of each type of coin.
Found 3 solutions by josgarithmetic, math_tutor2020, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
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There are three times as many nickels as dimes, and there are ten more quarters than dimes. If the total value of the coins is $40.00 then,...
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The money equation can be written all in one variable, d for dimes.

Simplify that and solve for d....
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answers:
225 nickels
75 dimes
85 quarters

Work Shown:

d = number of dimes
3d = number of nickels
d+10 = number of quarters

10d = value of the dimes (cents)
5(3d) = 15d = value of the nickels (cents)
25(d+10) = 25d+250 = value of the quarters (cents)

10d+15d+(25d+250) = 4000 cents aka $40
50d+250 = 4000
50d = 4000-250
50d = 3750
d = 3750/50
d = 75 dimes
3d = 3*75 = 225 nickels
d+10 = 75+10 = 85 quarters

Check:
225 nickels = 225*5 = 1125 cents = $11.25
75 dimes = 75*10 = 750 cents = $7.50
85 quarters = 85*25 = 2125 cents = $21.25
total = $11.25+$7.50+$21.25 = $40
The answers are confirmed.
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
A collection of nickels, dimes, and quarters is retrieved from a vending machine.
There are three times as many nickels as dimes, and there are ten more quarters than dimes.
If the total value of the coins is $40.00 then find the number of each type of coin.
~~~~~~~~~~~~~~~~~


            It may seem fantastic,  but the problem can be
            solved mentally,  without using equations. 


Take 10 quarters aside, for a minute.


Then the updated collection has three times as many nickels as dimes, 
and the same number of quarters as dimes and it is worth 

    40.00 - 10*0.25 = 40 - 2.50 = 37.50 dollars.


Now group the coins in the sets, combining 1 dime, three nickels and 1 quarter in each set.
According to the problem, it CAN BE DONE.


Each set is worth  10 + 3*5 + 25 = 50 cents; so, the number of sets is   = 75.


From this, we conclude that the original collection has 
75 dimes, 3*75 = 225 nickels and 75+10 = 85 quarters.      ANSWER

Solved.

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Good problem for a school  Math circle to give it to advanced students
and ask them to solve it  MENTALLY,  without using equations.


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If a Math teacher wants to bring up students with vivid mind, he (or she)
should give them such assignments from time to time.



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