SOLUTION: You have a spare change jar containing 22 coins consisting of nickels, dimes and quarters. If there is a total of $3.50 and there are as many quarters as there are nickels and dime

Question 894532: You have a spare change jar containing 22 coins consisting of nickels, dimes and quarters. If there is a total of $3.50 and there are as many quarters as there are nickels and dimes, how many dimes are there?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
n = no. of nickels
d = no. of dimes
q - no. of quarters
:
Write an equation for each statement
:
You have a spare change jar containing 22 coins consisting of nickels, dimes and quarters.
n + d + q = 22
:
If there is a total of $3.50
.05n + .10d + .25q = 3.50
:
and there are as many quarters as there are nickels and dimes,
q = n + d
In the first equation, replace n + d with q
q + q = 22
2q = 22
q = 11 quarters
:
how many dimes are there?
replace q with 11 in both equations
n + d + 11 = 22
subtract 11 from both sides
n + d = 11
and
.05n + .10d + .25(11) = 3.50
.05n + .10d = 3.50 - 2.75
.05n + .10d = .75
multiply by 10, use elimination with the 1st equation
1n + d = 11
.5n + d = 7.50
------------------subtraction eliminates d
.5n + 0 = 3.5
n = 3.5/.5
n = 7 nickels
:
Find d using the 1st original equation
7 + d + 11 = 22
d = 22 - 18
d = 4 dimes
:
:
Check this by finding the $ amt with these values
.05(7) + .10(4) + .25(11) =
.35 + .40 + 2.75 = 3.50

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