SOLUTION: Daniel has $2.90 in nickels, dimes and quarters. If he has three more nickels than dimes and twice as many dimes as quarters, how many of each does he have?

Question 597476: Daniel has $2.90 in nickels, dimes and quarters. If he has three more nickels than dimes and twice as many dimes as quarters, how many of each does he have?
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
.
[I] Define your variables
.
n = the number of nickels
d = the number of dimes
q = the number of quarters
.
.
[II] Create equations showing the given relationships
.
There are three more nickels than dimes.

.
There are twice as many dimes as quarters.
or
.
The total amount of money is $2.90
The value of the nickels is $0.05 times the number of nickels, or 0.05n
The value of the dimes is $0.10 times the number of dimes, or 0.10d
The value of the quarters is $0.25 times the number of quarters, or 0.25q
.

.
.
[III] Solve the system of equations.
I'll use the substitution method.
.
Substitute d+3 for n and d/2 for q into the value equation.
.

.
Simplify and solve for d.

.
The equation d=10 means that there are 10 dimes.
There are n = d+3 = 10+3 = 13 nickels.
There are d/2 = 10/2 = 5 quarters.
.
[IV] Check your work.
Do these coins add up to $2.90?
13 nickels is 6*13 = $0.65
10 dimes is 10*10 = $1.00
5 quarters is 5*25 = $1.25
$0.65 + 1.00 + 1.25 = $2.90
Check!
.
That's it!
.
Feel free to email me via gmail if the explanation is unclear.
.
Ms.Figgy
math.in.the.vortex@gmail.com

RELATED QUESTIONS
Mary has $5.00 in nickels, dimes, and quarters. If she has twice as many dimes as... (answered by ankor@dixie-net.com)

bill has $3.75 in quarters,dimes,and nickels. he has twice as many quarters as dimes and... (answered by rossiv53)

A boy has 93 cent in pennies, nickels, dimes, and quarters. He has two more quarters than (answered by EMStelley)

Judy has three more dimes than nickels and twice as many nickels as quarters. If... (answered by stanbon)

Jon has quarters, dimes, and nickels in his pocket. The value of his money is $1.75.... (answered by josgarithmetic)

Colin has pennies, nickels and dimes in his piggybank. He has twice as many nickels as... (answered by SwiftAlbatross)

roger has $3.10 consisting of quarters, dimes and nickels. He has twice as many quarters... (answered by JBarnum)

Sam has $3.15 in quarters nickels and dimes he has half as many quarters as he has dimes (answered by josgarithmetic,ikleyn,timofer,greenestamps,mccravyedwin,Edwin McCravy,MathTherapy)

Roger has $3.15 in quarters dimes and nickels he has twice as many quarters as dimes and... (answered by FrankM)