Question

At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two small fries have a total of 1,330 calories. How many calories does each item contain? Create two equations to model this situation using X and Y for your variables. Use a comma to separate your equations.

Answer 1

A cheeseburger contains 290 calories and a small fries contains 230 calories.

Step-by-step explanation:

Let X be the number of calories in a cheeseburger, and Y be the number of calories in a small fries.

From the given information, we can create two equations:

1. 4X + 5Y = 2310
2. 3X + 2Y = 1330

To solve this system of equations, we can use substitution or elimination. Let's use elimination:

• Multiply equation 1 by 3 and equation 2 by 4 to eliminate the X term:
• 12X + 15Y = 6930
• 12X + 8Y = 5320
• Subtract the second equation from the first equation:
• 12X + 15Y - 12X - 8Y = 6930 - 5320
• 7Y = 1610
• Divide both sides by 7:
• Y = 230
• Substitute the value of Y into either equation and solve for X:
• 3X + 2(230) = 1330
• 3X + 460 = 1330
• 3X = 870
• X = 290

Therefore, a cheeseburger contains 290 calories and a small fries contains 230 calories.

Answer 2

Let x = calories in a cheeseburger
Let y = calories in an order of small fries

Four cheeseburgers and five small fries have 2,310 calories. Therefore
4x + 5y = 2310 (1)

Three cheeseburgers and two small fries have 1,330 calories. Therefore
3x + 2y = 1330 (2)

Equations (1) and (2) model the given situation.

To solve, multiply (1) by 2, and multiply (2) by 5 to obtain
8x + 10y = 4620 (3)
15x + 10y = 6650 (4)

Subtract (3) from (4).
7x = 2030
x = 290
From (1), obtain
5y = 2310 - 4*290 = 1150
y = 230

Answer:
The two equations are
4x + 5y = 2310
3x + 2y = 1330

The solutions are x = 290, y = 230.