You need to set up two equations to solve this question and assign two variables. We will have a=adults and c=children. The first equation will be the total amount received from the tickets for both the adults and children which is 4(a) + 1.75(c) = $309.75. The second equation is total number of people attending of 105 made up of adults(a) and children(c). a + c = 105. We will rearrange this and rewrite it as a = 105-c by subtracting c from both sides of the equation. Now we will replace a in the first equation with 105 - c which will give us 4(105-c) + 1.75(c) = $309.75. We will now distribute the 4 to both the 105 and the -c which will give us the new equation of 420-4(c) + 1.75(c) = $309.75. Now we subtract 420 from both sides which gives us the new equation -4(c) + 1.75(c) = $309.75-$420.00. We can combine like terms on both sides of the equal sign which gives us -2.25(c) = -$110.25. We now divide both sides by -2.25 and get c = 49 children tickets. To find out how many adult tickets were sold you take 105-49 = 56 adult tickets. To check your answer you multiply 56 x $4.00 = $224.00 + $85.75 = total of $309.75. The $85.75 comes from 49 children tickets x $1.75. I hope this helps you with this problem but contact me if you need any further explanations.
