Question

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

Answer 1

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