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 budget 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.
E)None of the above.

Question

Quizplus · Accepted Answer

Let's start with the calorie limit: 
- 3400 calories per day 
- Each bag of pretzels has 600 calories 
- Each seafood salad has 200 calories

Let's use P to represent the number of bags of pretzels Quincy can eat and S to represent the number of seafood salads he can eat:

- Total calories = 600P + 200S 
- Total spending = 1P + 2S <= 14 (Quincy's daily budget)

Now we need to find the maximum values of P and S that satisfy both constraints.

First, let's look at the spending limit:

1P + 2S <= 14

If we set S = 0, we get:

1P <= 14

P <= 14 (maximum number of pretzel bags Quincy can buy with his entire budget)

So Quincy can buy at most 14 bags of pretzels with his entire budget.

Now let's look at the calorie limit:

600P + 200S <= 3400

Divide both sides by 200:

3P + S <= 17

If we set S = 0, we get:

3P <= 17

P <= 5.666...

But Quincy can't buy a fraction of a bag of pretzels. So he can buy at most 5 bags of pretzels to stay under his calorie limit.

We can also solve for S:

S <= 17 - 3P

If we set P = 4, we get:

S <= 5

So Quincy can also buy up to 5 seafood salads to stay under his calorie limit.

Therefore, the best choice is C: Quincy can consume up to 4 bags of pretzels and 5 seafood salads per day, spending 13 dollars in total and consuming exactly 3400 calories.

Quincy Lives on Pretzels and Seafood Salads