SOLUTION: Selena has some nickels, dimes and quarters. She has 1½ times as many dimes as nickels. She has 5 fewer quarters than nickels. If Selena has a total of $5.05, how many of each coin

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Question 947536: Selena has some nickels, dimes and quarters. She has 1½ times as many dimes as nickels. She has 5 fewer quarters than nickels. If Selena has a total of $5.05, how many of each coin does she have?
Found 3 solutions by josgarithmetic, macston, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
n, d, q the coins



Examine these equations for a while and you could think of a solution strategy.

Solve the first two equations in terms of n. They are of two variable each.
Simplify the money count, last or third equation. Substitute for d and q in the money count equation and first solve for the value of n.
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
N=Nickels; D=Dimes=1.5N; Q=Quarters=N-5
$0.05N+$0.10D+$0.25Q=$5.05 Substitute for D and Q
$0.05N+$0.10(1.5N)+$0.25(n-5)=$5.05
$0.05N+$0.15N+$0.25N-$1.25=$5.05 Add $1.25 to each side
$0.45N=$6.30 Divide each side by $0.45
N=14 ANSWER 1: There are 14 nickels.
D=1.5N=1.5(14)=21 ANSWER 2: There are 21 dimes.
Q=N-5=14-5=9 ANSWER 3: There are 9 quarters
CHECK
$0.05N+$0.10D+$0.25Q=$5.05
$0.05(14)+$0.10(21)+$0.25(9)=$5.05
$0.70+$2.10+$2.25=$5.05
$5.05=$5.05
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Selena has some nickels, dimes and quarters. She has 1½ times as many dimes as nickels. She has 5 fewer quarters than nickels. If Selena has a total of $5.05, how many of each coin does she have?


Let number of nickels be N

Then number of dimes = , or , or 

Number of quarters = N - 5 

We then have: 







.6N + .3N = 12.6 -------- Multiplying by LCD, 2

.9N = 12.6

N, or number of nickels = , or 

Number of dimes: , or 

Number of quarters: 14 – 5, or  

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