Question

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The cost of cheese varies directly with the number of pounds bought. If 2 pounds cost $8.40, find the cost of 3.5 pounds.

a. $12.50
c. $14.25
b. $10.75
d. $14.70

Answer 1

If 2 pounds cost $8.40, your number sense tells you 1 pound costs half as much, or $4.20.

Then 3.5 pounds will cost 3.5 times as much:
   3.5 × $4.20 = $14.70

The appropriate choice is
   d. $14.70


_____
You can do this one in your head if you take it a step farther and consider the cost of 1/2 pound of cheese. That will be $2.10. Then 3.5 pounds is 7 half-pounds, so the cost will be 7 × $2.10 = (7×$2) + (7×0.10) = $14 + .70.

Answer 2

We need to find the unit price, which is when x is one. Since the cost varies on the pounds, pounds is the independent variable, x. We do y/x to find the unit price.

8.40÷2=4.20

Since this is the unit price, we could multiply it by the pounds someone wants to buy to find out the price.

4.20×3.5
14.70

So, the price of 3.5 pounds is $14.70.