Question

Norman buys lunch for his employees at the El Camion Food Truck every Friday. Last week, he purchased 8 tacos and 5 burritos and paid $28.25. The week before, he bought 7 tacos and 7 burritos and paid $33.25. Write a SYSTEM of EQUATIONS to model Norman's food truck purchases for the last two weeks. Be sure to define your variables. SOLVE the system of equations to find the cost of ONE taco and ONE burrito.

Answer 1

1 taco costs $1.5 and 1 burrito costs $3.25

Explanation:

-Let t denote tacos and b denote burritos.

-The system of equations in the two weeks can then be expressed as below:

`8t+5b=28.25\ \ \ \ \ \ ...i\\\\7t+7b=33.25\ \ \ \ \ \ ...ii`

make t the subject of the formula in i and then substitute in ii to solve for both unknowns:

`8t=28.25-5b\\\\t=(1)/(8)(28.25-5b)\\\\\\\therefore 7t+7b=33.25\\\\(7)/(8)(28.25-5b)+7b=33.25\\\\\\24.71875-4.375b+7b=33.25\\\\8.53125=2.625b\\\\\\b=3.25\\\\t=(1)/(8)(28.25-5*3.25)=1.5`

Hence, 1 taco costs $1.5 and 1 burrito costs $3.25