Question 1028601: A jar has quarter and nickels with 76 coins. Total value is 10.80. Find the amount quarter and nickels Found 2 solutions by Edwin McCravy, fractalier:Answer by Edwin McCravy(20081) (Show Source):
Let the number of quarters be x
Let the number of nickels be y
Value Value
Type Number of of
of of EACH ALL
coin coins coin coins
-------------------------------------------
quarters x $0.25 $0.25x
nickels y $0.05 $0.05y
-------------------------------------------
TOTALS 76 ----- $10.80
The first equation comes from the second column.
x + y = 76
The second equation comes from the last column.
0.25x + 0.05y = 10.8
Get rid of decimals by multiplying every term by 100:
25x + 5y = 1080
So we have the system of equations:
.
We solve by substitution. Solve the first equation for y:
x + y = 76
y = 76 - x
Substitute (76 - x) for y in 25x + 5y = 1080
25x + 5(76 - x) = 1080
25x + 380 - 5x = 1080
20x + 380 = 1080
20x = 700
x = 35 = the number of quarters.
Substitute in y = 76 - x
y = 76 - (35)
y = 41 nickels.
Checking: 35 quarters is $8.75 and 41 nickels is $2.05
That's 76 coins.
And indeed $8.75 + $2.05 = $10.80
Edwin
You can put this solution on YOUR website! Call the number of quarters and nickels, q and n.
Then we write
q + n = 76 and the value equation is
25q + 5n = 1080 (we work in cents)
Now multiply the top one by five and subtract...we get
25q + 5n = 1080
-(5q + 5n = 380)
-----------------
20q = 700
q = 35 quarters which means there are
n = 41 nickels
