Question

A rancher raises calves that need to be given vaccinations. To give the vaccinations, she must hire several helpers. The rancher knows that the vaccinations cost $20.50 per calf and estimates that the cost to pay helpers is $5 per calf.

Which expressions represent the total cost of vaccinating x calves? Choose all that are correct.
A.
20.50x + 5.00x


B.
20.50 +5.00 divided by x



C.
20.50 + 5.00 + x


D.
(20.50 + 5.00)x


E.
X divided by 20.50 + 5.00


F.
(20.50 + 5.00)x divided by x

Answer 1

A and D

if the calfs were x=10
it would be 20.50*10+5*10
And D would use the distributive property

Answer 2

A., D.

Explanation:

The number of calves is x.

$20.50 per calf is 20.50x.

$5 per calf is 5x.

The total cost is the sum of those two costs: 20.50x + 5x.

A. 20.50x + 5x is exactly what we have above, so it is correct.

B.
`(20.50 + 5.00)/(x)` is not equivalent to our expression above, so it is correct.

C. 20.50 + 5.00 + x is not equivalent to our expression above, so it is incorrect.

D. (20.50 + 5.00)x

Apply the distributive property:

(20.50 + 5.00)x = 20.50x + 5.00x

This is equal to our expression above, so it is correct.

E.
`(x)/(20.50 + 5.00)` This is not equivalent to our expression above.

F.
`((20.50 + 5.00)x)/(x) = 20.50 + 5.00` This is not equivalent to our expression above.

Answer: A., D.