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 dinner for $17. If the total bill was $91, how many people ordered each type of dinner?

4 step method:

1. define variables

2. write the systems of equations

3. solve showing all steps

4. state your solution in your sentence

1.)

c=number of people that ordered chicken dinner

s=number of people that ordered steak dinner

2.)

c+s=6

148c+170s=910

3.)

now you would use elimination or substitution. In this specific problem, i think elimination would be best. Elimination is used to cancel out one variable. For this problem, i will eliminate s.

In order to do that, you need to multiply the top equation by - 170 in order to cancel out the positive 170 in the bottom equation.

-170 (c+s=6)

-170c+-170s=-1020

Now, you have

-170c+-170s=-1020

148c+170s=910

Now you cancel out the s variables and you are left with

-170c=-1020

148c=910

now you add the two equations together

-170c+148c=22c

-1020+910=110

Your new equation is 22c=110

now you divide both sides of the equation by 22 to get c alone

22c/22=110/22

c=5

now you plug in your answer for c in one of the original equations, to make it easier plug it into the top equation

5+s=6

now subtract 5 from both sides

s=1

5 people bought chicken dinners, and one person ordered steak dinner