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?

(a) System of equations: and

(b) One soda costs

(c) One taco costs

SOLUTION:

Given, Mrs. Galicia bought 3 tacos and 2 sodas and paid .  

The next day she went back and bought 5 tacos and 1 soda and paid .  

Let the cost of 1 tacos be m, and cost of 1 soda be n.

Now, We have to find  

(a) System of equations:  

3 tacos and 2 sodas cost

5 tacos and 1 soda cost

System of equations are  

Now,

So, substitute n in (1)

(b) cost of one soda

(c) cost of one taco

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

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