Question

The total cost of turkey, y, varies directly with the number of pounds of turkey purchased, x. A customer bought 2.4 pounds of turkey for $14.28. Determine the constant of variation and the total cost of 1.6 pounds of turkey. Move the correct answer to each box. Not all answers will be used.

Answer 1

The constant of variation is
`\boxed{\sf 5.95}`

The total cost of 1.6 pounds of turkey is
`\boxed{\sf \$9.52}`.

Explanation:

The problem states that the total cost of turkey,
`\sf y`, varies directly with the number of pounds of turkey purchased,
`\sf x`.

In a direct variation, the relationship is given by
`\sf y = kx`, where
`\sf k` is the constant of variation.

The customer bought 2.4 pounds of turkey for $14.28.

We can use this information to find the constant of variation (
`\sf k`):

`\sf 14.28 = k * 2.4`

Now, solve for
`\sf k`:

`\sf k = (14.28)/(2.4) = 5.95`

So, the constant of variation is
`\sf 5.95`.

Now, to find the total cost of 1.6 pounds of turkey (
`\sf y`), use the constant of variation (
`\sf k`):

`\sf y = k * x`

`\sf y = 5.95 * 1.6 \\\\ = 9.52`

Therefore, the constant of variation is
`\sf 5.95` and the total cost of 1.6 pounds of turkey is $9.52.

Answer 2

The constant of variation is 5.95.

The total cost of 1.6 pounds of turkey is $9.52.

Explanation:

The relationship between the total cost (y) and the number of pounds of turkey purchased (x) is given by the formula for direct variation:

`y = kx`

where k is the constant of variation.

From the information given, when x = 2.4 pounds, y = 14.28 dollars.

Substitute these values into the formula:

`14.28 = k * 2.4`

Now, solve for k:

`k = (14.28)/(2.4)`

`k = 5.95`

Therefore, the formula that relates the number of pounds of turkey purchased (x) to the total cost (y) is:

`y=5.95x`

To find the total cost for 1.6 pounds of turkey, substitute x = 1.6 into the formula:

`y = 5.95 * 1.6`

`y = 9.52`

Therefore, the total cost of 1.6 pounds of turkey is $9.52.