Elena is making a grape drink. the recipe calls for 2 parts grape juice concentrate to 6 parts water. elena would like to make 80 fluid ounces of the grape drink. how many fluid ounces of grape juice concentrate and water does elena need

20 oz of juice concentrate and 60 oz of water.

Explanation:

Translate the word statements into algebraic expressions to set a system of equations that you can solve.

1) Name the variables:

2) Statement one, 2 parts juice concentrate to 6 parts water, translates into a proportion:

    j / w = 2 / 6

3) Statement two, 80 oz of the drink, tanslates into an equality:

     j + w = 80

a) System:

                 j / w = 2 / 6

                 j + w = 80

b) Solve for w in the first equation: w = 6j / 2 = 3j

c) Substitute w in the second equation: j + 3j = 80

d) Combine like terms: 4j = 80

e) Use division property of equality: j = 20

f) Substitue in w = 3j: 3 = 3(20) = 60.

5) Solution: j = 20, w = 60.

6) Verify: