Question

sophia buys 9 tacos and 8 enchiladas for 78 dollars. anthony buys 2 tacos and 4 enchilladas for 24 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 $t$ = cost of 1 taco, $e$ = cost of 1 enchilada.

Step2: Set up equations

Equation 1 (Sophia): $9t + 8e = 78$
Equation 2 (Anthony): $2t + 4e = 24$

Step3: Simplify Equation 2

Divide by 2: $t + 2e = 12$, rearrange to $t = 12 - 2e$

Step4: Substitute into Equation 1

$9(12 - 2e) + 8e = 78$
Expand: $108 - 18e + 8e = 78$
Simplify: $108 - 10e = 78$

Step5: Solve for $e$

$-10e = 78 - 108$
$-10e = -30$
$e = \frac{-30}{-10} = 3$

Step6: Solve for $t$

Substitute $e=3$ into $t = 12 - 2e$:
$t = 12 - 2(3) = 12 - 6 = 6$

Answer:

Part A: 6
Part B: 3