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
----------------------------------------------------------------------------------------------------------
(-8T + 3T) + (-2D + 2D) = (-30.5 + 13)
(-5T = -17.5) / -5
T = 3.5
Thus, each taco costs $3.50.
----------------------------------------------------------------------------------------------------------
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.