systems of equation

Question

Two groups of student go out to lunch .the first group orders 2 burritos and 5 taco and the bill 19.50 . the secound group 5 burritos and 2 tacos and the bill comes to 22,50 .what is the cost of each burrito and each tacos?

Answer 1

Hi Narissa,

Let X = cost of a burrito

Let Y = cost of a taco

We can now form the two system of equations

based on the given information.

2X + 5y = 19.50

5X + 2y = 22.50

We can now solve for Y with the two system

of equations.

5(2X + 5y) = 5(19.50)

-2(5X + 2Y) = -2(22.50)

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10X + 25Y = 97.50

-10X - 4Y =-45.00

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21Y = 52.50

Y = 2.50

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We can now substitue Y in one of the equations

and solve for X.

5X + 2(2.50) = 22.50

5X + 5 = 22.50

5X = 17.50

X = 3.50

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Each burrito costs $3.50.

Each taco costs $2.50