Quincy lives on pretzels and seafood salads. The price of pretzels is 1 dollar p

Question

Quincy lives on pretzels and seafood salads. The price of pretzels is 1 dollar per bag and the price of seafood salads is 2 dollars each. Quincy allows himself to spend no more than 14 dollars a day on food. He also restricts his consumption to 3,400 calories per day. There are 600 calories in a bag of pretzels and 200 calories in a seafood salad. If he spends his entire money bud get each day and consumes no more calories than his calorie limit, he can consume up to

a. 2 bags of pretzels per day but no more.

b. 5 seafood salads per day but no more.

c. 4 bags of pretzels per day but no more.

d. 5 bags of pretzels per day but no more.

The directions state to simply choose the one best answer. Can you please show your work and logic too!

Explanation / Answer

Answer

Price Of Pretzels(Pp) = $1 and Price of Seafood Salad(Ps) and his Income = 14 and Suppose Quantity of Pritzel be P and Seafood be S

So His Budget Line Equation will be P + 2S = 14-------------------------(1)

Now Calorie Per Pritzel be 600 and Calorie per seafood salad = 200 and Maximum Calorie = 3400.

Hence we have the Following inequality to represents his Calorie Intake :

600P + 200S <= 3400 => 3P + S <= 17. Lets Take Maximum calorie she can consumethen We have the following equation = 3P + S = 17------------------------(2).

Solving (1) and (2) we get :

3P + S = 17 and P + 2S = 14

Solving this we get 5P = 20 => P = 4 and Hence S = 5.

Hence She can consume 5 pritzel and still she is within her calorie limit. Niw If she takes 1 more Pritzel then he has to consume 5 pritzel and 4 seafood Then her total calorie intake will be 5*600 + 4*200 = 3800.

Which is beyonds her calorie limit hence he can maximum consume 4 pritzel But no more..

So He can consume Maximum Pretzels = 4.

Hencce The correct answer is (c). 4 bags of pretzels per day but no more.

NOTE = He can maximum consume 7 seafoods ina day. If he consumes 7 seafood then he will spend $14 and her total calorie intake wil be 200*7 = 1400

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