SOLUTION: Plato has 58 coins in nickels, dimes, and quarters. The number of nickels is three less than twice the nuber of dimes. The total value of the coins is $7.40. How many of each coin

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Question 278092: Plato has 58 coins in nickels, dimes, and quarters. The number of nickels is three less than twice the nuber of dimes. The total value of the coins is $7.40. How many of each coin does Plato have?
**please include the work to get the answer, too
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Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Plato has 58 coins in nickels, dimes, and quarters.
The number of nickels is three less than twice the number of dimes.
The total value of the coins is $7.40.
How many of each coin does Plato have?
:
Let n = no. of nickels
Let d = no. of dimes
Let q = no. of quarters
:
Write an equation for each statement
:
"Plato has 58 coins in nickels, dimes, and quarters."
n + d + q = 58
:
"The number of nickels is three less than twice the number of dimes."
n = 2d - 3
:
"The total value of the coins is $7.40."
.05n + .10d + .25q = 7.40
:
From the 2nd equation, we know that n = (2d-3)
Replace n in the 1st equation
(2d-3) + d + q = 58
3d + q = 58 + 3
3d + q = 61
q = (61-3d); use this form for substitution
:
Do the same in the 3rd equation
.05(2d-3) + .10d + .25q = 7.40
.10d - .15 + .10d + .25q = 7.40
.20d + .25q = 7.40 + .15
.20d + .25q = 7.55
replace q with (61-3d)
.20d + .25(61-3d) = 7.55
.20d + 15.25 - .75d = 7.55
.20d - .75d = 7.55 - 15.25
-.55d = -7.70
d =
d = 14 dimes
:
Find the number of nickels
n = 2d - 3
n = 2(14) - 3
n = 25 nickels
:
How many of each coin does Plato have?
Use the 1st equation to find q
n + d + q = 58
25 + 14 + q = 58
q = 58 - 39
q = 19 quarters
;
:
You can check solution in the total$ equation:
.05(25) + .10(14) + .25(19) =