Laura has $4.50 in dimes and quarters. She has 3 more dimes than quarters. How many quarters does she have?

1 Answer
Jun 2, 2015

Let's name a the number of dimes and b the number of quarters.
A dime is $0.1 and a quarter is $0.25

Thus : 0.1a+0.25b=4.5
And we know that she has 3 more dimes than quarters
Thus : a=b+3
We just replace the value of a in the equation :

0.1*(b+3)+0.25b=4.5
0.1b+0.3+0.25b=4.5
0.1b+0.25b=4.5-0.3 ( we substract 0.3 on each side )
0.35b=4.2

b=4.2/0.35 ( we divide by 0.35 on each side )

b=12 : Laura has 12 quarters

We can now get a :

0.1a+0.25b=4.5
0.1a+0.25*12=4.5
0.1a+3=4.5
0.1a=4.5-3 ( we substract 3 on each side )
0.1a=1.5

a=1.5/0.1 ( we divide by 0.1 on each side )

a=15 : Laura has 15 dimes

We can now verify :
15*0.1+12*0.25=1.5+3=4.5 : correct !
And 15=12+3, so Laura has 3 more dimes than quarters : perfect