Question

colin buys 9 tacos and 7 enchiladas for 77 dollars. colton buys 4 tacos and 8 enchilladas for 44 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

$$9t + 7e = 77$$
$$4t + 8e = 44$$

Step3: Simplify second equation

Divide by 4: $t + 2e = 11$, so $t = 11 - 2e$

Step4: Substitute into first equation

$$9(11 - 2e) + 7e = 77$$
$$99 - 18e + 7e = 77$$
$$99 - 11e = 77$$

Step5: Solve for $e$

$$-11e = 77 - 99$$
$$-11e = -22$$
$$e = 2$$

Step6: Solve for $t$

$$t = 11 - 2(2) = 11 - 4 = 7$$

Answer:

Part A: 7
Part B: 2