Question

Gopi loves cheeseburgers and hamburgers, and they have fat and calories as follows: cheeseburgers contain 13 13 grams of fat and 330 330 calories; hamburgers contain 18 18 grams of fat and 265 265 calories. How many cheeseburgers and hamburgers did Gopi eat when 111 111 grams of fat and 2050 2050 calories were consumed

Answer 1

Let's assume Gopi ate x cheeseburgers and y hamburgers.

From the given information, we can create two equations:

Equation 1: 13x + 18y = 111 (equation representing the total grams of fat consumed)
Equation 2: 330x + 265y = 2050 (equation representing the total calories consumed)

We can solve these equations simultaneously to find the values of x and y.

Multiply Equation 1 by 10 and Equation 2 by 3 to eliminate the decimals:
130x + 180y = 1110
990x + 795y = 6150

Multiply Equation 1 by 795 and Equation 2 by 180 to eliminate the y variable:
10335x + 14310y = 87930
59400x + 47700y = 369000

Now, subtract the second equation from the first equation:
(-59400x + 10335x) + (-47700y + 14310y) = 87930 - 369000
(-49065x) + (-33390y) = -281070

Divide the entire equation by -1 to simplify:
49065x + 33390y = 281070

Now, add this equation to Equation 2:
59400x + 47700y + 49065x + 33390y = 369000 + 281070
108465x + 81090y = 650070

Solve this equation for x and y using a calculator or algebraic methods:
x = 4
y = 3

Therefore, Gopi ate 4 cheeseburgers and 3 hamburgers.