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23 December, 02:49

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

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  1. 23 December, 04:53
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    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
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