SOLUTION: One hundred gallons of 70% disinfectant is mixed with a certain amount of 90% disinfectant to yield a batch of 75% disinfectant. How much 90% disinfectant was used?

Question 1125126: One hundred gallons of 70% disinfectant is mixed with a certain amount of 90%
disinfectant to yield a batch of 75% disinfectant. How much 90% disinfectant was used?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

Let x be the amount of the 90% disinfectant (in gallons). Your equation is pure disinfectant + pure disinfectant = total pure disinfectant, or 0.7*100 + 0.9x = 0.75*(100+x), 0.7*100 + 0.9x = 0.75*100 + 0.75x 0.9x - 0.75x = 0.75*100 - 0.7*100 x = = 33.333 gallons. Answer. 33.333 gallons of the 90% disinfectant. Check. 0.7*100 + 0.9*33.333 = 100 gallons of the pure disinfectant; 0.75*(100+33.333) = 100 gallons of the pure disinfectant. ! Correct !

Solved.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = number of gallons of 90% disinfectant.

equation becomes:

.7 * 100 + .9 * x = .75 * (100 + x)

simplify to get 70 + .9 * x = 75 + .75 * x.

subtract 70 from both sides of the equation and subtract .75 * x from both sides of the equation to get:

.9 * x - .75 * x = 75 - 70

simplify to get .15 * x = 5

solve for x to get x = 5 / .15 = 33 and 1/3.

you are mixing 100 gallons of 70% solution with 33 and 1/3 gallons of 90% solution.

the total gallons is 133 and 1/3.

the total disinfectant in that 133 and 1/3 gallons is .70 * 100 + .9 * (33 and 1/3) = 100 gallons.

the percent disinfectant in that total solution is 100 / (133 + 1/3) = .75 * 100 = 75%.

solution looks good.

solution is that 33 and 1/3 gallons of 90% disinfectant solution was used.

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