Question

A collection of dimes and quarters is worth $6.50. There are 35 coins in all. How many dimes are there. Work it out with two equations.

Answer 1

d=dimes, q=quarters
First equation: d+q=35
Second equation: 0.1d+0.25q=6.50
d+q=35 can be changed into the equation q=-d+35
Then, plug the first equation into the second equation. This is the method of substitution.
0.1d+0.25(-d+35)=6.50
0.1d-0.25d+8.75=6.50
-0.15d+8.75=6.50
-8.75 -8.75
-0.15d=-2.25
/-0.15 /-0.15
d=15
There are 15 dimes. You can check this answer by plugging in 15 as d in the first equation. Then you would get 20 quarters. These two numbers satisfy both equations.

Answer 2

d + q = 35....d = 35 - q
0.10d + 0.25q = 6.50

0.10(35 - q) + 0.25q = 6.50
3.50 - 0.10q + 0.25q = 6.50
-0.10q + 0.25q = 6.50 - 3.50
0.15q = 3
q = 3 / 0.15
q = 20 <=== 20 quarters

d + q = 35
d + 20 = 35
d = 35 - 20
d = 15 <=== 15 dimes