To find the number of calories in one beef burrito and one cheeseburger, we need to solve the system of linear equations given by the problem. Let’s denote the number of calories in one beef burrito as [tex]\( B \)[/tex] and the number of calories in one cheeseburger as [tex]\( C \)[/tex].
We are given two pieces of information:
1. One beef burrito and two cheeseburgers together provide 2870 calories.
2. Two beef burritos and one cheeseburger together provide 3370 calories.
From this information, we can set up the following system of equations:
[tex]\[ B + 2C = 2870 \][/tex]
[tex]\[ 2B + C = 3370 \][/tex]
To solve this system, we can use the method of substitution or elimination. Here, we'll use the elimination method.
Step 1: Multiply the first equation by 2 to align the coefficients of [tex]\( B \)[/tex]:
[tex]\[ 2(B + 2C) = 2 \times 2870 \][/tex]
This simplifies to:
[tex]\[ 2B + 4C = 5740 \][/tex]
Step 2: Subtract the second equation from this new equation:
[tex]\[ (2B + 4C) - (2B + C) = 5740 - 3370 \][/tex]
This simplifies to:
[tex]\[ 4C - C = 5740 - 3370 \][/tex]
[tex]\[ 3C = 2370 \][/tex]
Step 3: Solve for [tex]\( C \)[/tex]:
[tex]\[ C = \frac{2370}{3} \][/tex]
[tex]\[ C = 790 \][/tex]
So, each cheeseburger contains 790 calories.
Step 4: Substitute the value of [tex]\( C \)[/tex] back into the first equation to solve for [tex]\( B \)[/tex]:
[tex]\[ B + 2(790) = 2870 \][/tex]
[tex]\[ B + 1580 = 2870 \][/tex]
[tex]\[ B = 2870 - 1580 \][/tex]
[tex]\[ B = 1290 \][/tex]
So, each beef burrito contains 1290 calories.
Hence, the caloric contents are:
- One beef burrito contains 1290 calories.
- One cheeseburger contains 790 calories.
