Question

johnny's cafe serves desserts. one serving of ice cream and two servings of blueberry pie provides 860 calories. three servings of ice cream and two servings of blueberry pie provides 1340 calories. find the caloric content of each item. solve manually, showing all work.

Answer 1

One serving of ice cream at Johnny's cafe contains 240 calories, and one serving of blueberry pie contains 310 calories. The caloric content was found using a system of linear equations and the elimination method to solve for each item's calories.

Step-by-step explanation:

To determine the caloric content of each item at Johnny's cafe, we can set up a system of equations based on the information given:

• One serving of ice cream and two servings of blueberry pie provides 860 calories.
• Three servings of ice cream and two servings of blueberry pie provides 1340 calories.

Let's denote the number of calories in one serving of ice cream as I and in one serving of blueberry pie as P. We can then write the following equations:

1. I + 2P = 860
2. 3I + 2P = 1340

We can solve this system using the substitution or elimination method. The elimination method is more straightforward here:

1. Multiply the first equation by 3: 3I + 6P = 2580
2. Subtract the second equation from this new equation: (3I + 6P) - (3I + 2P) = 2580 - 1340
3. Simplify the equation: 4P = 1240
4. Divide by 4 to find P: P = 310

Now that we know P, the number of calories in a serving of blueberry pie, we can find I by substituting P back into one of the original equations:

1. I + 2(310) = 860
2. I + 620 = 860
3. I = 860 - 620
4. I = 240

Therefore, one serving of ice cream contains 240 calories, and one serving of blueberry pie contains 310 calories.