Question

Blake has some quarters and dimes. He has 20 coins worth a total of $2.90. How many of each type of coin does he have?

Answer 1

Q=number of quarters
d=number of dimes

so the value of 1 quarter=0.25 and 1 dime=0.10 so therefor the total value would be
0.25q+0.1d=2.9

total number of coins=20
q+d=20

solve
we have
0.25q+0.1d=2.9 and
q+d=20
multiply the first equation by 10
2.5q+1d=29

so we have
q+d=20
2.5q+d=29

multiply first by -1 and add
-q-d=-20
2.5q+d=29  +
1.5q+0d=9
1.5q=9
multipliy both sides by 2
3q=18
divide by 3
q=6
subsitute
q+d=20
6+d=20
ubtract 6
d=14

14 dimes
6 quarters

Answer 2

6 quarters
14 dimes
This took me 20 minutes to solve... :))