SOLUTION: Okay I'm stumped on this problem. I have tried to figure out the equation but I keep geting stuck. The problem is: "A chemist has a 90% solution of sulfuric acid and a 70% solution

Question 581415: Okay I'm stumped on this problem. I have tried to figure out the equation but I keep geting stuck. The problem is: "A chemist has a 90% solution of sulfuric acid and a 70% solution of the same acid. How many gallons of each must be mixed in order to make 200 gallons of 75% solution?"
Here's what I know: I know that x is the amount of the 90% solution and that y would be the amount of the 70% solution. I think that the equation would be .90x + .70y = .75 and that the other equation is x+y=200. but I am not sure I did that right and I keep getting fractions as my answer. Help please.
Found 2 solutions by nerdybill, ankor@dixie-net.com:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Okay I'm stumped on this problem. I have tried to figure out the equation but I keep geting stuck. The problem is: "A chemist has a 90% solution of sulfuric acid and a 70% solution of the same acid. How many gallons of each must be mixed in order to make 200 gallons of 75% solution?"
Here's what I know: I know that x is the amount of the 90% solution and that y would be the amount of the 70% solution. I think that the equation would be .90x + .70y = .75 and that the other equation is x+y=200. but I am not sure I did that right and I keep getting fractions as my answer. Help please.
.
You almost had it right. It should have been:
Let x = amount (gallons) of 90% solution
and y = amount (gallons) of 70% solution
.
x+y=200 (equation 1)
.90x + .70y = .75(200) (equation 2)
.
Solving equation 1 for y
x+y=200
y=200-x
Substitute above into equation 2:
.90x + .70y = .75(200)
.90x + .70(200-x) = .75(200)
.90x + 140-.70x = 150
.20x + 140 = 150
.20x = 10
x = 50 gallons (of 90% solution)
.
70% solution:
x+y=200
50+y=200
y = 150 gallons

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
"A chemist has a 90% solution of sulfuric acid and a 70% solution of the same acid.
How many gallons of each must be mixed in order to make 200 gallons of 75% solution?"
:
We can do it this way
:
Let x = amt of 90% solution
the resulting amt is to be 200 gal, therefore
(200-x) = amt of 70% solution
:
.90x + .70(200-x) = .75(200)
solve for x, to get the 90% amt, then subtract that from 200 to get the 70%
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