Question

A vendor sells tacos and burritos. One family buys 3 tacos and 2 burritos for $9.25. Another family buys 7 tacos and 4 burritos for $19.75. Find the cost of each item.

Answer 1

Taco: $1.25

Burrito: $2.75

Explanation:

Let x = tacos

y = burritos

Since the first family bought 2 burritos, we multiply y by 2; we multiply x by 3 since they bought 3 tacos.

3x + 2y = 9.25

We do basically the same thing for the other family

7x + 4y = 19.75

We'll use elimination method to solve this

7x + 4y = 19.75

3x + 2y = 9.25

Multiply the bottom equation by -2

7x + 4y = 19.75

(3x + 2y = 9.25)-2

7x + 4y = 19.75

-6x - 4y = -18.5

Now subtract the equations and we get this

x = 1.25

A taco costs $1.25

Plug the new x into one of the original equations

3(1.25) + 2y = 9.25

3.75 + 2y = 9.25

- 3.75 - 3.75

2y = 5.5

2y/2 = 5.5/2

y = 2.75

A burrito costs $2.75