Question

Armand is planning a crawfish boil for the weekend. Crawfish are like tiny lobsters, about 3 to 4 in. long. They are especially popular in Louisiana. Crawfish are cooked in a pot of boiling water with spicy seasoning, called a “crawfish boil.” Every 10 lb of crawfish requires 24 oz of seasoning. (a) What is the unit rate and what does this number mean? (b) How much seasoning would Armand need for 30 lb of crawfish? Explain or show your work. (c) What is the maximum number of pounds of crawfish that can be cooked with 36 oz of seasoning? Explain or show your work.

Answer 1

Every 10 lb of crawfish requires 24 oz of seasoning.

(a) What is the unit rate and what does this number mean?

Unit rate = 24 oz / 10lb = 2.4 oz / lb .This means that we need 2.4 oz of seasoning for every pound of crawfish.

(b) For 1 pound we need = 2.4 oz

For 30 pounds we need =
`2.4*30=72`

We need 72 oz of seasoning.

(c) 2.4 oz of seasoning is required for = 1 lb

1 oz of seasoning is required for =
`(1)/(2.4)` lb

36 oz of seasoning is required for =
`(1)/(2.4)*36=15` lb

Hence 15 pounds of crawfish can be cooked in 36 oz of seasoning.

Answer 2

For this case we have that for every 10 pounds of crawfish 24 ounces of seasoning are required, then:

10 pound crawfish ----------> 24 ounces of seasoning

If we want to know the unit rate we divide both quantities, that is:

`Unit Rate = \frac {24} {10}`

`Unit Rate = 2.4` ounces of seasoning per pound of crawfish.

That means that 2.4 ounces of seasoning are necessary to prepare a pound of crawfish.

Now, if you want to prepare 30 pounds of crawfish, to know the amount of seasoning necessary, we make a rule of three:

10 pound crawfish ----------> 24 ounces of seasoning

30 pounds crawfish ----------> x ounces of seasoning

Where x represents the amount of seasoning needed to prepare 30 pounds of crawfish. Resolving we have:

`x = \frac {(30 * 24)} {10}`

`x = \frac {720} {10}`

`x = 72`

Thus, 72 ounces of seasoning are needed to prepare 30 pounds of crawfish.

On the other hand, if you want to know the amount of pounds of crawfish that can be cooked with 36 ounces of seasoning, we make another rule of three:

10 pound crawfish ----------> 24 ounces of seasoning

y pounds crawfish ------------> 36 ounces of seasoning

Where "y" represents the amount of pounds of crawfish that can be prepared with 36 ounces of seasoning. Resolving we have:

`y = \frac {(36 * 10)} {24}`

`y = \frac {360} {24}\\y = 15`

Thus, you can prepare maximum 15 pounds of crawfish with 36 ounces of seasoning.

Answer:

A)
`Unit Rate = 2.4` ounces of seasoning per pound of crawfish. To prepare a pound of crawfish, 2.4 ounces of seasoning are necessary.

B)
`x = 72`. You need 72 ounces of seasoning to prepare 30 pounds of crawfish.

C)
`y = 15`. Maximum 15 pounds of crawfish can be prepared with 36 ounces of seasoning.