15 students preordered the year book and 9 students paid full price.
<u>Solution:
</u>
Given that
Cost of pre-ordered year book =
each
Cost of full price of year book =
each
Number of students in Mr. Hillman's class purchased yearbooks = 24
Total price spent by 24 students to purchase year book = ![\$975](https://tex.z-dn.net/?f=%5C%24975)
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 = ![24-x](https://tex.z-dn.net/?f=24-x)
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 = ![x\times38 = 38x](https://tex.z-dn.net/?f=x%5Ctimes38%20%3D%2038x)
Money spent by students who paid full price = number of students paid full price x Cost of 1 full price year book =
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
![\Rightarrow 975=38 x+1080-45 x](https://tex.z-dn.net/?f=%5CRightarrow%20975%3D38%20x%2B1080-45%20x)
On solving above expression for x, we get
![\begin{array}{l}{\Rightarrow 975-1080=38 x-45 x} \\\\ {\Rightarrow-105=-7 x} \\\\ {\Rightarrow \frac{-105}{-7}=x} \\\\ {\Rightarrow x=15}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5CRightarrow%20975-1080%3D38%20x-45%20x%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow-105%3D-7%20x%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow%20%5Cfrac%7B-105%7D%7B-7%7D%3Dx%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow%20x%3D15%7D%5Cend%7Barray%7D)
Number of student pre-ordered year book = ![x=15](https://tex.z-dn.net/?f=x%3D15)
Number of students paid full price = ![24-x = 24-15 = 9](https://tex.z-dn.net/?f=24-x%20%3D%2024-15%20%3D%209)
Hence 15 students pre-ordered the year book and 9 students paid full price.