How much candy at $1.16 a pound should be mixed with candy worth 86¢ a pound in order to obtain a mixture of 60 pounds of candy worth a dollar a pound?

sdentatoiz

sdentatoiz

Answered question

2022-09-09

How much candy at $1.16 a pound should be mixed with candy worth 86¢ a pound in order to obtain a mixture of 60 pounds of candy worth a dollar a pound?

Answer & Explanation

Vicente Macias

Vicente Macias

Beginner2022-09-10Added 15 answers

We have two types of candy. Let x be the candy costing $1.16 a pound. Let y be the candy costing $0.86 per pound. (We'll work in dollars for the problem.)
We want to end up with 60 pounds of candy so we know that:
Equation (1): x+y=60
We know that we want the average cost to be $1 per pound. To get the average cost we need to know the total cost and divide by the total pounds.
Total cost: 1.16x + 0.86y
Total pounds: 60
Average cost we want: 1
So, 1.16 x + 0.86 y 60 = 1
We can rearrange that to get a second equation:
Equation (2): 1.16x+0.86y=60
multiply equation (1) by −0.86 to get equation (3):
Equation (3): −0.86x−0.86y=−51.6
Add equation (2) and equation (3), the y cancels out:
0.3x=8.4
divide through by 0.3:
x=28
Substitute into equation (1): 28 + y = 60 y = 32
So we want 28 pounds of the candy costing $1.16 and 32 pounds of the candy costing $0.86.

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