One serving of grapes has 100 calories and 21 grams of carbohydrates. One serving of raspberries has 60 calories and 9 grams of carbohydrates.

How many servings must be consumed to get 500 calories and 87 grams of carbohydrates? Fill in the missing information for the system of equations that could be used to answer the question.

Ax + 60y = 500
21x + 9y = B

What is the value for B?

A = 100,

B = 87.

And the solution to the system us

,  

Step-by-step explanation:

Let us call the servings of grapes and he servings of raspberries.

One serving of grapes has 100 calories and one serving of raspberries has 60 calories, and since together 500 calories must be consumed, we have:

Furthermore, one serving of grapes has 21 grams of carbohydrates and one serving of raspberries has 9 grams, and if at total of 87 grams of carbohydrates are consumed, we have

.

Thus, the system of equations we have are

(1).

(2). .

Here we see that

.

The numbers of servings that must be consumed are the solutions of the system.

The solutions to the system can be found by solving for in equation(2), and substituting its value equation (1):

putting this into equation (2), we solve for :