Percentages word problem..

[UofUmath]

How much 90 percent vinegar do you have to add to a gallon of 5 percent vinegar to get 20 percent vinegar

I've been trying to solve this problem forever and I just can't do it. I emailed my instructor and she sent me the equation

0.05+0.9x/1+x=0.20

I thought from there I would be able to solve it, but I'm confused about the rules of eliminating things and what I should do first. Am I allowed to subtract the 0.05 from the 0.20 first? Or is do I need to multiply by the reciprocal? I'm really confused, please help. And I would prefer if I wasn't given the answer, I want to understand the concept so I can do it for myself.

[stapel_eliz]

How much 90 percent vinegar do you have to add to a gallon of 5 percent vinegar to get 20 percent vinegar

I've been trying to solve this problem forever and I just can't do it.

To learn, in general, how to set up and solve "mixture" type word problems, try here.

I emailed my instructor and she sent me the equation

0.05+0.9x/1+x=0.20

I will guess that you mean (or that your instructor meant) "(0.05 + 0.9x) / (1 + x) = 0.20". The first step in solving this rational equation will be to multiply through by "1 + x" to get rid of the fraction:

. . . . .0.05 + 0.9x = 0.2(1 + x)

I'll bet you solve the linear equation from there!