Intermediate Algebra Question?

Question

Eight liters of a 40% solution of acid will be mixed with some 70% solution to get a 50% solution. How much of the 70% solution should be used?

Please show work or tell me how to do this problem.

Thank you.

Answer 1

i little over 12%

Answer 2

phoenix answered the question very well with that equation i couldn't do. i solved it conceptually, maybe this might help put a picture in your mind.

the difference between 40% and 70% is 30%. you want to increase the concentration by 10% to 50%. this means it will need more 40% solution than 70% solution, because if you put in 8 liters of 70% the concentration would be in the middle, 55%.

increasing it by that 10% is 1/3 of that 30% difference. so the 70% should be 1/3 of the mixture and the 40% should be 2/3 of the mixture.

so 8 liters is 2/3 of what? 12 liters. that means 4 liters of 70% solution should be used.

if this helps, good luck

Answer 3

Let x=number of litres of 70% solution

0.4*8+0.7x=0.5(x+8)

you can take it from there..