The table below shows the ticket rates for whale watching trips offered by beluga fun tours:

age ticket price
under 3 years free
3 to 12 years $34
over 12 years $45

on a certain day, the company took 103 people on whale watching trips. there were 64 children aged 12 and under, of which some children were under 3 years. if x represents the number of children under 3 years, which equation can be used to find the value of x, where c represents the total amount of money collected from tickets that day?

You know that there are 64 children under 12 and 103 total people. This means that the number of people over the age of 12 has to be (103 - 64). To find the amount of money earned from this group of people, just multiply by the price for people over the age of 12: $45. Thus, one part of your equation has to be (103 - 64)∙45. 

The second part of the equation is a bit more difficult. You know that x = the number of children under 3, and those children are free. All we need to find is the number of children between 3 and 12 who have to pay and then multiply by their price: $34. So, just subtract the free children from the total children and multiply by 34: (64 - x)∙34. 

Put this all together and you get (64 - x)∙34 + (103 - 64)∙45