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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?

Respuesta :

Answer:

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

Step-by-step 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

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