SOLUTION: Eight gallons of salt consists of 35% salt. It is the result of mixing a 50% solution with a 30% solution. How many gallons of each of the solutions was used? The corresponding mod

Question 1081639: Eight gallons of salt consists of 35% salt. It is the result of mixing a 50% solution with a 30% solution. How many gallons of each of the solutions was used? The corresponding modeling system is
X+y=8
.5x+.3y=.35(8)
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
(1)
(2)
----------------------
(2)
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)
-----------------------

and
(1)
(1)
---------------------
2 gallons of the 50% solution are needed
6 gallons of the 30% solution are needed
-------------------------------------
check:
(2)
(2)
(2)
(2)
OK
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Eight gallons of salt consists of 35% salt.
It is the result of mixing a 50% solution with a 30% solution.
How many gallons of each of the solutions was used?
The corresponding modeling system is
X + y = 8
.5x+.3y=.35(8)
:
X + y = 8
.5x+.3y= 2.8
multiply by 2, subtract from the 1st equation
x + y = 8
x +.6y = 5.6
---------------Subtraction eliminates x find y
0 + .4y = 2.4
y = 2.4/.4
y = 6 gallons of 30% solution
then
x = 2 gallons of 50% solution
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