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Difficulty: EasySystems of Linear Equations

A food truck sells tacos and burritos. On Tuesday, the food truck sold a total of 120 tacos and burritos. The number of tacos sold, tt, was 20 more than the number of burritos sold, bb. This situation is represented by the system of equations below:

t+b=120t + b = 120
t=b+20t = b + 20

How many burritos did the food truck sell on Tuesday?

Answer: 50

Answer

The food truck sold 50 burritos on Tuesday.
To find the number of burritos sold, bb, we substitute t=b+20t = b + 20 into the first equation t+b=120t + b = 120, giving (b+20)+b=120(b + 20) + b = 120. Combining like terms yields 2b+20=1202b + 20 = 120. Subtracting 20 from both sides results in 2b=1002b = 100. Finally, dividing both sides by 2 gives b=50b = 50. Thus, the food truck sold 50 burritos on Tuesday.

Step-by-Step Solution

1
Substitute the expression for tt from the second equation into the first equation
(b+20)+b=120(b + 20) + b = 120
To eliminate the variable tt and set up an equation with only one variable, bb.
2
Combine like terms on the left side of the equation
2b+20=1202b + 20 = 120
To simplify the equation for solving.
3
Subtract 20 from both sides of the equation
2b=1002b = 100
To isolate the variable term on one side of the equation.
4
Divide both sides of the equation by 2
b=50b = 50
To solve for the variable bb representing the number of burritos.

Key Concept

Solving systems of linear equations using the substitution method
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Topics

Systems of Linear Equations

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