Pre-orders for the yearbook cost $38 each and full price cost $45 each. If 24 students in Mr. Hillman's class purchased yearbooks for a total of $975, how many students pre-ordered and how many paid full price?

15 students preordered the year book and 9 students paid full price. Solution: Given that  Cost of pre-ordered year book = [tex]\$38[/tex] each Cost of full price of year book = [tex]\$45[/tex] each Number of students in Mr. Hillman's class purchased yearbooks = 24 Total price spent by 24 students to purchase year book = [tex]\$975[/tex]Need to determine number of students pre-ordered and number of students paid full price. Let assume number of student pre-ordered year book = x As out of 24, x students pre-ordered the yearbook , so remaining are the ones who paid full price So number of students paid full price = [tex]24-x[/tex]Money spent by students who pre-ordered the book = number of student pre-ordered year book multiplied by Cost of 1 pre-ordered year book = [tex]x\times38 = 38x[/tex]Money spent by students who paid full price = number of students paid full price x Cost of 1 full price year book = [tex](24-x)\times 45 = 1080-45x[/tex] Total price spent by 24 students to purchase year book = Money spent by students who pre-ordered the book + Money spent by students who paid full price [tex]\Rightarrow 975=38 x+1080-45 x[/tex]On solving above expression for x, we get [tex]\begin{array}{l}{\Rightarrow 975-1080=38 x-45 x} \\\\ {\Rightarrow-105=-7 x} \\\\ {\Rightarrow \frac{-105}{-7}=x} \\\\ {\Rightarrow x=15}\end{array}[/tex]Number of student pre-ordered year book = [tex]x=15[/tex]Number of students paid full price = [tex]24-x = 24-15 = 9[/tex]Hence 15 students pre-ordered the year book and 9 students paid full price.