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

Answer: 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:

j: parts of juice concentrate w: parts of water

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

4) Solve the system to find how many oz of juice concentrate and water Elena needs:

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:

j / w = 20 / 60 = 2 / 6 ⇒ right j + w = 20 + 60 = 80 ⇒ right