Louis V. answered • 09/02/19
Professional and Insightful Tutor With Over 21 Years of Experience!
What you would do is to set up a system of equations, as there are two variables for the tickets. Let's say x = the adult tickets and y = the children's tickets. Based on this, we can set up two different equations. We can say there are a total of 26 tickets sold. On that basis, x + y = 26. Then, also we are given the price per ticket, as $8.50/adult ticket and $5.50 per child's ticket. This equation works out to 8.50x + 5:50y = 194.
First we would solve one equation for x or y. Let's take the simpler equation, and say y = 26 - x.
We then plug that in for y in the second equation, using subsitution.
In this case we have 8.50x + 5.50(26 - x) = 194.
Using the distributive property this works out to: 8.50x + 5.50*26 - 5.50x = 194.
Then we combine like terms: (8.50x - 5.50x) + 143 = 194. **We also subtract 194 from 143 and get 51.**
This gives us 3x = 51. We then divide each side by 3 to get our answer for x.
x = 17 then. Finally we go to the first equation and y = 26 - 17 = 9. So we would have to have 17 adult tickets and 9 childrens' tickets sold to equal $194.00 worth of tickets sold. Problem solved!
As you can see I am more wordy. But the devil is in the details, and getting all of the steps correct.
