Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost a total of $228. Write and solve a system of equations to find how many children and how many adults were in the group.

nicekikah 2021-03-02 Answered
Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost a total of $228. Write and solve a system of equations to find how many children and how many adults were in the group.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

yagombyeR
Answered 2021-03-03 Author has 92 answers

1.First we have to set up the equations for the problem. The first equation represents the total amount of people in the group. While the second equation represents the cost. In both equations x represents the number of adults while y represents the number of children.
x+y=11
22x+15y=228
2.Next you must solve the first equation for y.
y=11x
3.Now you must substitute the value of y into the second equation.
22x+15(11x)=228
Next you must multiply every thing in the parentheses by 15.
22x+16515x=228
4.Next you subtract 15x from 22x because they are like terms.
22x15x+165=228
7x+165=228
5.Now you must subtract 165 from 228, so that x is on a side by its self.
7x=228165
7x=63
6.Now you must divide 63 by 7, so that you find the value of one x not seven.
x=637
x=9
7.Now place the value you found for x into the original first equation.
9+y=11
8.Now subtract 9 from 11 in order to solve for y.
y=119
y=2
Finally check your answers by placing the values you found for x and y into the second equation.
(229)+(152)=228
198+30=228
228=228
There were 9 adults and children.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more