Algebra please solve

Question

one fruit punch has 40% juice and another is 80% fruit juice how much of 40% points should be mixed with 10 gal of 80% punch to Crest a fruit punch that is 50% fruit juice

Answer 1

The question needs a rewrite. What do "40% points" and "to Crest a fruit punch" mean?

I'll answer what I think you are asking, which is how much 40% fruit punch do you need to add to 10 gallons of 80% fruit punch to make a 50% fruit punch.

1] (10 gal of 80% Fruit Punch) + (X gal of 40% Fruit Punch) = (10+X gal of 50% Fruit Punch).

Solve for X. :-)

The punch is part water and part fruit juice:

2] (2 gal H2O + 8 gal FJ) + (0.6X gal H2O + 0.4X gal FJ) = 0.5(10+X) gal H2O + 0.5(10+X) gal FJ

3] ==================================== = 5 gal H2O + 0.5X gal H2O + 5 gal FJ + 0.5X gal FJ

Combine like terms - keep water and juice separate and avoid results with negative numbers:

4] (8-5) gal FJ + (0.6-0.5)X gal H2O = (5-2) gal H2O + (0.5-0.4)X gal FJ

5] 3 gal FJ + 0.1X gal H2O = 3 gal H2O + 0.1X gal FJ

Now put the "X" terms on the same side:

6] 3 gal H2O + 3 gal FJ = 0.1X gal H2O + 0.1X gal FJ

Factor out coefficients:

7] 3 gal (H2O + FJ) = 0.1X gal (H20 + FJ)

Cancel the terms in parens:

8] 3 gal = 0.1X gal

9] X = 30 gal

So you need 30 gallons of 40% fruit punch to add to 10 gallons of 80% fruit punch in order to make a solution of 50% fruit punch, which will amount to 40 gallons of punch. Plenty for a nice big party. You can plug 30 into equation 2 above to prove the solution.

Don't you just love algebra?!