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?

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