Question

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.

Answer 1

12.6-10.5=2.1(1.5 pounds) 2.1 divided by 3 = 0.7x2= 1.4 Therefore one pound of cheese is £1.40

Answer 2

The cost of one pound of the cheese is $4.2 .

The equation for direct variation is y = kx.

Where k is constant of variation .

Explanation:

Let us assume that the pound of cheese be x.

Let us assume that the cost of cheese be y.

As given

The cost of cheese varies directly with the number of pounds purchased.

Thus

`y\propto x`

y = kx

Where k is the constant of variation.

Nola purchased 2.5 pounds of cheese for $10.50.

y = 10.50 , x = 2.5

Put in the y = kx

10.50 = 2.5k

`k = (10.50)/(2.5)`

k = 4.2

Her mother purchased 3 pounds of the same cheese for $12.60.

y = 12.60 , x = 3

Put in the y = kx

12.60 = 3k

`k = (12.60)/(3)`

k = 4.2

Therefore the constant of variation is 4.2 .

As given

One pound of cheese costs.

x = 1 , k = 4.2

Put in the y = kx

y = 1 × 4.2

= $4.2

Therefore the cost of one pound of the cheese is $4.2 .