Question

xavier buys 7 tacos and 6 enchiladas for 32 dollars. john buys 8 tacos and 2 enchiladas for 22 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

$$7t + 6e = 32$$
$$8t + 2e = 22$$

Step3: Simplify second equation

Divide the second equation by 2:
$$4t + e = 11$$
Rearrange to isolate $e$: $e = 11 - 4t$

Step4: Substitute into first equation

Substitute $e = 11 - 4t$ into $7t + 6e = 32$:
$$7t + 6(11 - 4t) = 32$$

Step5: Solve for $t$

Expand and simplify:
$$7t + 66 - 24t = 32$$
$$-17t = 32 - 66$$
$$-17t = -34$$
$$t = \frac{-34}{-17} = 2$$

Step6: Solve for $e$

Substitute $t=2$ into $e = 11 - 4t$:
$$e = 11 - 4(2) = 11 - 8 = 3$$

Answer:

Part A: 2
Part B: 3