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12 December, 02:49

A small candy store makes three types of party mixes. The first type contains 2020 % nonpareils and 8080 % peanut clusters, while the second type contains 5050 % peanut clusters and 5050 % chocolate-covered raisins. The third type consists of 4040 % nonpareils, 3030 % peanut clusters, and 3030 % chocolate-covered raisins. If the store has 130130 pounds of nonpareils, 140140 pounds of peanut clusters, and 120120 pounds of chocolate-covered raisins available, how many pounds of each type of party mix should be made?

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  1. 12 December, 04:48
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    First type

    nonpareils=43376.66 pounds

    peanut clusters = 70070 pounds

    Second type

    peanut clusters = 43793.75 pounds

    chocolate-covered raisins = 75075 pounds

    Third type

    nonpareils = 86753.33 pounds

    peanut clusters = 26276.25 pounds

    chocolate-covered raisins = 45045 pounds

    Step-by-step explanation:

    Types of party mixes;

    nonpareils

    peanut clusters

    chocolate-covered raisins

    Store has

    130130 pounds of nonpareils

    140140 pounds of peanut clusters

    120120 pounds of chocolate-covered raisins

    Ratio of % ages nonpareils of first and third types is given below;

    2020:4040

    or

    1:2

    Sum of ratios = 1+2=3

    So %age share of First type nonpareils = 1 * 130130/3=43376.66 pounds

    and %age share of Third type = 2 * 130130/3=86753.33 pounds

    Ratio of peanut clusters in each type

    8080 : 5050 : 3030

    or 808:505:303

    sum of ratios = 808+505+303=1616

    %age share of peanut clusters of First type = 808 * 140140/1616=70070 pounds

    %age share of peanut clusters of Second type = 505 * 140140/1616=43793.75 pounds

    %age share of peanut clusters of third type = 303 * 140140/1616=26276.25 pounds

    Ratio of chocolate-covered raisins in second and third types;

    5050: 3030

    or

    505:303

    Sum of ratios = 505+303=808

    %age of chocolate-covered raisins of second type = 505*120120/808=75075 pounds

    %age ratio of chocolate-covered raisins of third type = 303 * 120120/808=45045 pounds
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