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?

Question

bahrom7893 · Answer

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

anonymous · Answer

please tryy!

bahrom7893 · Answer

btw do u have the answer to it?

bahrom7893 · Answer

bcuz it would make life so much easier

anonymous · Answer

i think its 80 for a and 40 for b

bahrom7893 · Answer

k tnx

anonymous · Answer

yupp

anonymous · Answer

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.

anonymous · Answer

You then use substitution

$$A=(-B(84/120)+72/120)/66/120$$

anonymous · Answer

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

anonymous · Answer

its finee!

anonymous · Answer

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

anonymous · Answer

why is b negative

anonymous · Answer

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.

anonymous · Answer

wait was my answer correct? im honestly so confused

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

You distribute the 66/120 and get

(-B(84/120)+(72/120)+B(84/120)=72/120

anonymous · Answer

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.

anonymous · Answer

Sorry

anonymous · Answer

itss okayy!