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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.

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

Answer :

Answer:

The constant of variation is 5.95.

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

Step-by-step 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:

[tex]y = kx[/tex]

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:

[tex]14.28 = k \times 2.4[/tex]

Now, solve for k:

[tex]k = \dfrac{14.28}{2.4}[/tex]

[tex]k = 5.95[/tex]

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

[tex]y=5.95x[/tex]

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

[tex]y = 5.95 \times 1.6[/tex]

[tex]y = 9.52[/tex]

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

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Rewritten by : Barada

Answer:

The constant of variation is [tex]\boxed{\sf 5.95}[/tex]

The total cost of 1.6 pounds of turkey is [tex]\boxed{\sf \$9.52}[/tex].

Step-by-step explanation:

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

In a direct variation, the relationship is given by [tex]\sf y = kx[/tex], where [tex]\sf k[/tex] 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 ([tex]\sf k[/tex]):

[tex]\sf 14.28 = k \times 2.4[/tex]

Now, solve for [tex]\sf k[/tex]:

[tex]\sf k = \dfrac{14.28}{2.4} = 5.95[/tex]

So, the constant of variation is [tex]\sf 5.95[/tex].

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

[tex]\sf y = k \times x[/tex]

[tex]\sf y = 5.95 \times 1.6 \\\\ = 9.52[/tex]

Therefore, the constant of variation is [tex]\sf 5.95[/tex] and the total cost of 1.6 pounds of turkey is $9.52.