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Select your answer If three tacos and two drinks cost $13.00, and four tacos and one drink costs $15.25, how much does a taco cost?

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Answer:

Each taco costs $3.50.

Explanation:

We can determine how much a taco costs using a system of equations, where:

  • T represents the cost of one taco,
  • and D represents the cost of one drink.

For each equation, the sum of the costs for the tacos and drinks equals the total cost:

(price * number of tacos) + (price * number of drinks) = total cost.

First equation:

Since three tacos and two drinks cost $13.00, our first equation is given by:

3T + 2D = 13

Second equation:

Since four tacos and one drink cost $15.25, our second equation is given by:

4T + D = 15.25

Method to solve: Elimination:

First, we wan multiply the second equation by -1, which will allow us to eliminate the Ds since 2D - 2D = 0:

-2(4T + D = 15.25)

-8T - 2D = -30.5

Now we can add -8T - 2D = -30.5 and 3T + 2D = 13 to eliminate D and solve for T (the cost of one taco):

-8T - 2D = -30.5

+

3T + 2D = 13

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(-8T + 3T) + (-2D + 2D) = (-30.5 + 13)

(-5T = -17.5) / -5

T = 3.5

Thus, each taco costs $3.50.

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Optional: Find the cost of each drink to check the validity of the answer:

Finding the cost of each drink:

Before we can check that our answer for the cost of each taco is correct, we first need to find the cost of each drink by plugging in 3.50 for T in the first equation (3T + 2D = 13):

3(3.50) + 2D = 13

(10.5 + 2D = 13) - 10.5

(2D = 2.5) / 2

D = 1.25

Thus, each drink costs $1.25.

Checking the solutions in both equations:

Now we can check the validity of our answers by plugging in 3.5 for T and 1.25 for D in both equations in our system and seeing if we get 13 and 15.25 on both sides of the equation:

Checking 3.5 for T and 1.25 for D in 3T + 2D = 13:

3(3.5) + 2(1.25) = 13

10.5 + 2.5 = 13

13 = 13

Checking 3.5 for T and 1.25 for D in 4T + D = 15.25:

4(3.5) + 1.25 = 15.25

14 + 1.25 = 15.25

15.25

Thus, our answers are correct and we've correctly determine the cost of one taco.

User Mohamed Anser Ali
by
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