SOLUTION: A change machine contains nickels, dimes, and quarters. There are 75 coins in the machine, and the value of the coins is $7.25. There are 5 times as many nickels as dimes. Find the

Question 105059: A change machine contains nickels, dimes, and quarters. There are 75 coins in the machine, and the value of the coins is $7.25. There are 5 times as many nickels as dimes. Find the number of coins of each type in the machine.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
:
A change machine contains nickels, dimes, and quarters.
:
Just write an equation for each statement:
:
"There are 75 coins in the machine,"
n + d + q = 75
:
"the value of the coins is $7.25."
.05n + .10n + .25q = 7.25
:
" There are 5 times as many nickels as dimes."
n = 5d
:
Find the number of coins of each type in the machine.
:
Substitute 5d for n in the 1st equation:
5d + d + q = 75
6d + q = 75
q = (75-6d); use this for substitution later
:
Substitute 5d for n in the 2nd equation:
.05(5d) + .10d + .25q = 7.25
.25d + .10d + .25q = 7.25
.35d + .25q = 7.25
:
In the above equation substitute (75-6d) for q:
.35d + .25(75-6d) = 7.25
.35d + 18.75 - 1.5d = 7.25
.35d - 1.5d = 7.25 - 18.75
-1.15d = -11.5
d = -11.5/-1.15
d = +10 dimes
:
Find the nickels from n = 5d
n = 5(10)
n = 50 nickels
:
Find q using the 1st equation:
50 + 10 + q = 75
60 + q = 75
q = 75 - 60
q = 15 quarters
:
:
Check our solutions on the 2nd equation:.
.05(50) + .10(10) + .25(15) =
2.50 + 1.00 + 3.75 = 7.25; confirms our solutions
:
Did this makes sense to you? A lot of steps but each one is logical and simple.
Any questions?
RELATED QUESTIONS
A change machine contains nickels, dimes, and quarters. There are 75 coins in he machine, (answered by nyc_function)

A change maching contains nickels,dimes, and quarters. There are 75 coins in the machine, (answered by Edwin McCravy)

Need help with systems of equations using matrices. Don't know how to set up this... (answered by ankor@dixie-net.com)

I need a walkthrough on a word problem ( i think they are called trinomeals)... i... (answered by ReadingBoosters)

A vending machine has $41.25 in it. There are 255 coins total and the machine only... (answered by fractalier)

A vinding machine has $41.25 in it. there are 255 coins total and the machine only... (answered by fractalier)

A vending machine has 41.25 in it. There are 255 coins total and the machine only takes... (answered by fractalier)

A vending machine has $41.25 in it. There are 225 coins total and the machine only... (answered by Nate)

A vending machine has $41.25 in it. There are 255 coins total and the machine only... (answered by ewatrrr)