your family goes to a restaurant for dinner. there are 6 people in your family. some order the chicken dinner for $14.80 and some order the steak for $17. if the total bill was $91, how many people ordered chicken and how many ordered steak?

5 ordered chicken, and 1 ordered steak

Step-by-step explanation:

let's make c the number that ordered the chicken, and s the number that ordered steak. we're going to make an equation to solve for it:

14.8 c + 17 s = 91

We are in a situation where if someone orders chicken, they cannot have also ordered steak, and vice versa. This means we can make c or s equal to (6 - s) or (6 - c) respectively.

I will choose to replace s with (6 - c)

14.8c + 17 (6 - c) = 91

simplify

14.8c - 17 c + 102 = 91

subtract 102 from both sides and simplify cs

-2.2c = - 11

divide by - 2.2

c = 5

This means that 5 people ordered chicken, and 1 ordered steak, bringing the total to 14.8 * 5 + 17 * 1 = 74 + 17 = 91

If you do the math the other way (replacing c with (6-s), you get the same answers (c = 5, s = 1)

(14.80) (5) = 74

6-5 = 1

(17) (1) = 17

74 + 17 = 91

5 family members orders chicken, and only one orders steak.