Question

trey buys 4 tacos and 8 enchiladas for 40 dollars. kaylee buys 5 tacos and 2 enchilladas for 18 dollars. part a: enter the cost for one taco. part b: enter the cost for one enchilada. a. enter answer b. enter answer

Explanation:

Step1: Define variables

Let \( t \) be the cost of one taco (in dollars) and \( e \) be the cost of one enchilada (in dollars).

Step2: Set up equations

From Trey's purchase: \( 4t + 8e = 40 \) (Equation 1)
From Kaylee's purchase: \( 5t + 2e = 18 \) (Equation 2)

Step3: Simplify Equation 1

Divide Equation 1 by 4: \( t + 2e = 10 \) (Equation 3)

Step4: Solve for \( t \) from Equation 3

\( t = 10 - 2e \) (Equation 4)

Step5: Substitute Equation 4 into Equation 2

\( 5(10 - 2e) + 2e = 18 \)
Expand: \( 50 - 10e + 2e = 18 \)
Simplify: \( 50 - 8e = 18 \)
Subtract 50: \( -8e = 18 - 50 = -32 \)
Divide by -8: \( e = \frac{-32}{-8} = 4 \)

Step6: Find \( t \) using Equation 4

Substitute \( e = 4 \) into Equation 4: \( t = 10 - 2(4) = 10 - 8 = 2 \)

Answer:

Part A: 2
Part B: 4