Question

Mary has a total of 23 coins made up of nickels and quarters that made a sum of $3.15. How many more nickels than quarters does she have?
A) 10
B) 3
C) 8
D) 7
E) none of these

Answer 1

Nickels n
quarters q
I: 3.15=n*0.05+q*0.25
II: n+q=23

isolate n in II:
n+q=23
n=23-q

substitute n in I:
3.15=n*0.05+q*0.25=
3.15=(23-q)*0.05+q*0.25
3.15=(23-q)*(1/20)+(q/4)
3.15=(23/20)-q/20+(q/4)
3.15=1.15-(4*q/20)
2=q/5
10=q

insert q=10 into II:
n+q=23
n+10=23
n=13

so c) 3 more nickels than quarters