Bill mixes candy costing 45cents per pound with candy costing 65cents a pound. A 7-pound box of the mix costs $3.65. How much of each kind of candy should Bill use?

Bill should use 4.5 pounds of the candy costing 45 cents and 2.5 pounds of the candy costing 65 cents.

Step-by-step explanation:

With the information provided, you can say that the sum of the pounds of each type of candy is equal to 7, which can be expressed as:

x+y=7

Also, the statement indicates the 7 pound box costs $3.65 and you can say that the sum of the results of multiplying the price of each candy for the number of pounds is equal to $3.65, which is:

0.45x+0.65y=3.65

You have the following equations:

x+y=7 (1)

0.45x+0.65y=3.65 (2)

Now, you have to solve for x in (1):

x=7-y (3)

Then, you have to replace (3) in (2):

0.45(7-y)+0.65y=3.65

3.15-0.45y+0.65y=3.65

0.20y=0.50

y=0.50/0.20

y=2.5

Finally, you can replace the value of y in (3) to find x:

x=7-y

x=7-2.5

x=4.5

According to this, the answer is that Bill should use 4.5 pounds of the candy costing 45 cents and 2.5 pounds of the candy costing 65 cents.

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step-by-step explanation:

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