Question

3. Mrs.Galicia bought 3 tacos and 2 sodas and paid $9.75. The next day she went back and bought 5 tacos and 1 soda and paid $12.75.

(a) Write and solve a system of equations that model the problem. Show all your work.
(b) How much was one soda?
(c) How much was one taco?

Answer 1

a) 3x + 2y = 9.75, 5x + y = 12.75 is the required system of equations.

b) The cost of 1 soda = $1. 5

c) The cost of 1 taco = $2.25

Explanation:

Let the cost of each taco = $x

Let the cost of each soda = $y

Now, according to the question:

3x + 2y = $9.75

5x + y = $12.75 are the required system of equations.

Now, substituting the value of y = 12.75 - 5x in (1).

⇒The equation 3x + 2y = 9.75 becomes 3x + 2(12.75 -5x) = 9.75

or, 3x - 10x + 25.5 = 9.75

or, -7x = -15.75

⇒ x = 15.75/7 = 2.25

Hence, the cost of 1 taco = $x = $2.25

Now, y = 12.75 - 5x

= 12.75 - 5(2.25) = 12.75 - 11.25 = = 1.5

or, y = $1.5.

Hence, the cost of 1 soda = $y = $1.5