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.
