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Answer:
Store used 7.5 pounds of gummy candy, 2.5 pounds of jelly beans, and 3 pounds of hard candy.
Step-by-step explanation:
Let the amount of gummy candy be 'x'.
Let the amount of jelly beans be 'y'.
Let the amount of hard candy 'z'.
Now Given:
Sue is buying 13 pound of mixture.
So we can say that;
But Given:
The mixture calls for three times as many gummy candy pieces as jelly beans.
Substituting the value of x in above equation we get;
Also Given:
cost of gummy candy = $1.20
cost of jelly beans = $2.00
cost of hard candy = $2.60
Total Cost of mixture = $21.80
Now Total Cost of mixture is equal to cost of gummy candy multiplied amount of gummy candy plus cost of jelly bean multiplied amount of jelly bean plus cost of hard candy multiplied amount of hard candy.
framing in equation form we get;
But
So
Now Multiplying by both side by 10 we get;
Now Multiplying equation 1 by 14 we get;
Now Subtracting equation 3 from equation 2 we get;
Now Substituting value of z in equation 1 we get;
Now also;
Hence Store used 7.5 pounds of gummy candy, 2.5 pounds of jelly beans, and 3 pounds of hard candy.