Etch Clean Graphics uses one cleanser that is 25 percent acid and a second that is 50 percent acid. How many liters of each should be mixed to get a 10L of solution that is 40 percent acid?

Answer 1

You can use Elimination or Substitution to do this. ( 2 variable equation)

Let x= 25% acid

Let y= 50% acid

We need two equations in order to solve this problem

first we need amount of liters of x plus amount of liters of y to give 10L

Then we need how much x plus how much y to give a total of 40 percent solution in 10L

so we get

x+y=10 ========Eqn 1

0.25x+0.50y=10(0.4)======Eqn 2

By SUBSTITUTION

Get rid of decimals to make it easier to deal with, for equation 2 multiply by 100

we get

25x+50y=400

Solve equation 1 for x ( or y if you like it doesnt matter)

we get x=-y+10

Let x equal this in equation 2

So we have

25(-y+10)+50y=400

-25y+250+50y=400

25y+250+400

25y=150

y=6

Now we have to solve for x

Take any of your original equations and solve for x

(first on is easiest)

x+y=10

x+6=10

x=4

Therefore we need 6 liters of 50% acid and 4 liters of 25% acid to get a solution of 10L of 40% acid

By ELIMINATION

Same sort of steps we have our equations

x+y=10

.25x+.50y=.4(10) =====> 25x+50y=400

We now want to get a variable with the same coefficient but opposite as to "eliminate it" since 25 is smaller than 50 we will use this but we want the opposite sign so multiply first equation by -25

so we get

-25x-25y=-250 ( now add the two equations)

25x+50y=400

gives

0x+25y=150 (now solve for y)

y=6

Now plug y in to original equation to find x ( once again use first its easier but either would give the correct answer)

x+y=10

x+6=10

x+4

Hope this helps