A bag contains 31 coins, some dimes and some quarters. The total amount of money in the bag is $4.45. How many dimes and how many quarters are in the bag?
_____dimes
_____quarters
we know that
1 quarter=$0.25
1 dime=$0.10
Let
x -----> the number of quarters
y ----> the number of dimes
we have that
x+y=31 ------> equation A
0.25x+0.10y=4.45 -----> equation B
Solve the system of equations
Isolate the variable x in equation A
x=31-y ------> equation C
Substitute equation C in equation B
so
0.25(31-y)+0.10y=4.45
solve for y
7.75-0.25y+0.10y=4.45
0.25y-0.10y=7.75-4.45
0.15y=3.30
y=22 dimes
Find the value of x
x=31-22
x=9 quarters
therefore
the answer is
22 dimes
9 quarters