## anonymous 5 years ago Question: you want to mix two brands of juice together to produce 120 gallons of a 3/5 cranberry juice blend. Brand A contains 11/20 cranberry juice and Brand B contains 7/10 cranberry juice. How much of each brand should you mix together?

1. bahrom7893

will try to get to this, helpin someone at the moment

2. anonymous

3. bahrom7893

btw do u have the answer to it?

4. bahrom7893

bcuz it would make life so much easier

5. anonymous

i think its 80 for a and 40 for b

6. bahrom7893

k tnx

7. anonymous

yupp

8. anonymous

SO what you do is try and figure out how much each Brand contains in cranberry juice in a fraction where 120 gal is the denominator. So A has 66/20 B has 84/120 You make an equation then A(66/230)+ B(84/120)= 72/120 72/120 is 3/5 A and B in the equation are our variables, or the things we can change or that can change.

9. anonymous

You then use substitution \[A=(-B(84/120)+72/120)/66/120\]

10. anonymous

Sorry the value next to A in the equation is 66/120 not 66/230. I Dnt Know what I was thinking.

11. anonymous

its finee!

12. anonymous

So you simplify what A equals A=(-B(84/120)+72/120)/66/120 since you are dividing by fractions it is the same as saying A=(-B(84/120)+72/120) times 120/66

13. anonymous

why is b negative

14. anonymous

So what you do is substitute what you found A to be in terms of B into the equation. You then only have B as a variable in the equation. Solve for B. Now you still d0on't know what A is exactly in numbers. Plug in the exact value for B.

15. anonymous

wait was my answer correct? im honestly so confused

16. anonymous

You plug B into one of the equations you have that involve the variable A. You probably want to use the one that has A equals something, because you already have A isolated.

17. anonymous

A=-B(84/66) + (72/66) The 120s cancel

18. anonymous

Then you could plug what A equals into the equation A(66/120) + B(84/120)=72/120 you get (-B(84/66)+ (72/66)) (66/120) + B(84/120)=72/120

19. anonymous

You distribute the 66/120 and get (-B(84/120)+(72/120)+B(84/120)=72/120

20. anonymous

Ummmmnh I just realized that I must be solving it wrong. Because the equation that I last gave you comes out to 0=0, which is true, but not what we need.

21. anonymous

Sorry

22. anonymous

itss okayy!