Lee has 35 dimes and quarters that total $5.00. Solve the system of equations to find how many dimes and how many quarters he has.

Question

d+q=35
0.1d+0.25q=5

Please show your work thanks

Answer 1

d+q=35 ....(1)
0.1d+0.25q=5
multiply the second by 20 to get
2d+5q=100 ....(2)
Substitute d=35-q from (1)
70-2q+5q=100
3q=30
q=10
d=25

Another way to calculate (mentally) is as follows:
Assume all dimes: 35*0.1=3.5
There is $1.50 available to change quarters for dimes at 15 cents a piece. So we change 10 of them to get 10 quarters and (35-10)=25 dimes.