Question 1054128: Barbara has some dimes and quarters. If she has 25 coins worth a total of $2.95, how many of each type of coin does she have? Answer by Edwin McCravy(20054) (Show Source):
Let the number of dimes be x
Let the number of quarters be y
Value Value
Type Number of of
of of EACH ALL
coin coins coin coins
-------------------------------------------
dimes x $0.10 $0.10x
quarters y $0.25 $0.25y
-------------------------------------------
TOTALS 25 ----- $2.95
The first equation comes from the second column.
x + y = 25
The second equation comes from the last column.
0.10x + 0.25y = 2.95
Get rid of decimals by multiplying every term by 100:
10x + 25y = 295
So we have the system of equations:
.
We solve by substitution. Solve the first equation for y:
x + y = 25
y = 25 - x
Substitute (25 - x) for y in 10x + 25y = 295
10x + 25(25 - x) = 295
10x + 625 - 25x = 295
-15x + 625 = 295
-15x = -330
x = 22 = the number of dimes.
Substitute in y = 25 - x
y = 25 - (22)
y = 3 quarters.
Checking: 22 dimes is $2.20 and 3 quarters is $0.75
That's 25 coins.
And indeed $2.20 + $0.75 = $2.95
Edwin
