Question

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?

Answer 1

Answer:

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