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nola purchased 2.5 pounds of cheese for $10.50. her mother purchased 3 pounds of the same cheese for $12.60. the cost of cheese varies directly with the number of pounds purchased. complete the equations for direct variation and tell how much one pound of cheese costs.
y= ?
cheese cost per pound? = $

Since the total cost of cheese varies directly with the number of pound purchased, it is safe to assume that the cost per pound is constant.

Let us further assume that y is the total cost and x is the number of pounds bought. We must first get the cost per pound to complete the equation for direct variation.

cost per pound = total cost / pounds bought
cost per pound = $10.50 / 2.5 pounds
cost per pound = $4.20

to check if the above answer is correct, let us use the 2nd purchase.

cost per pound = total cost / pounds bought
cost per pound = $12.60 / 3 pounds
cost per pound = $4.20

Therefor, the cheese costs $4.20 per pound.

The direct variation equation is

y = $4.20x

where the y is the total cost; x is the number of pounds bought; and $4.20 is the constant or k.