Question

Jasmine is training for an upcoming fitness competition and is trying to find a breakfast

combination that meets her nutritional needs of 950 calories and 25 grams of protein. One
serving of cereal has 200 calories and 2 grams of protein. She also enjoys peanut butter
which contains 180 calories and 8 grams of protein per serving. How many servings of each
type of food should she eat to meet her nutritional needs?
a. Define your variables.
b. Write an equation that relates the number of servings of cereal and the number of
servings of peanut butter to the total number of calories she needs for breakfast.
c. Write an equation that relates the number of servings of cereal and the number of
servings of peanut butter to the total amount of protein she needs for breakfast.

Answer 1

Jasmine should eat 3 servings of cereal and 2 servings of peanut butter to meet her nutritional needs of 950 calories and 25 grams of protein respectively.

Step-by-step explanation:

To solve this problem, we can define the variables as follows:

Let x be the number of servings of cereal.

Let y be the number of servings of peanut butter.

The equation that relates the number of servings of cereal and the number of servings of peanut butter to the total number of calories she needs for breakfast is:

200x + 180y = 950

The equation that relates the number of servings of cereal and the number of servings of peanut butter to the total amount of protein she needs for breakfast is:

2x + 8y = 25

To solve these two equations, we can use the method of substitution or elimination. Let's use the method of elimination:

Multiply the first equation by 2 and the second equation by 200 to get:

400x + 360y = 1900

400x + 1600y = 5000

Subtract the second equation from the first equation to eliminate x:

1200y = 3100

Divide both sides of the equation by 1200 to solve for y:

y = 3100/1200 = 2.5833 (approximately)

Since we cannot have a fraction of a serving, Jasmine should eat 3 servings of cereal (x = 3) and 2 servings of peanut butter (y = 2) to meet her nutritional needs.