Let the number of quarters be x
Let the number of dimes be y
Value Value
Type Number of of
of of EACH ALL
coin coins coin coins
-------------------------------------------
quarters x $0.25 $0.25x
dimes y $0.10 $0.10y
-------------------------------------------
TOTALS 84 ----- $13.80
The first equation comes from the second column.
x + y = 84
The second equation comes from the last column.
0.25x + 0.10y = 13.80
Get rid of decimals by multiplying every term by 100:
25x + 10y = 1380
So we have the system of equations:
.
We solve by substitution. Solve the first equation for y:
x + y = 84
y = 84 - x
Substitute (84 - x) for y in 25x + 10y = 1380
25x + 10(84 - x) = 1380
25x + 840 - 10x = 1380
15x + 840 = 1380
15x = 540
x = 36 = the number of quarters.
Substitute in y = 84 - x
y = 84 - (36
y = 48 dimes.
Checking: 36 quarters is $9.00 and 48 dimes is $4.80
That's 84 coins.
And indeed $9.00 + $4.80 = $13.80
Edwin