Question

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?

Answer 1

15 students preordered the year book and 9 students paid full price.

Solution:

Given that  

Cost of pre-ordered year book = $\ 38$ each

Cost of full price of year book = $\ 45$ each

Number of students in Mr. Hillman's class purchased yearbooks = 24

Total price spent by 24 students to purchase year book = $\ 975$

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 = $24-x$

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 = $x\times38 = 38x$

Money spent by students who paid full price = number of students paid full price x Cost of 1 full price year book = $(24-x)\times 45 = 1080-45x$

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

$\Rightarrow 975=38 x+1080-45 x$

On solving above expression for x, we get

$\begin{array}{l}{\Rightarrow 975-1080=38 x-45 x} \\\\ {\Rightarrow-105=-7 x} \\\\ {\Rightarrow \frac{-105}{-7}=x} \\\\ {\Rightarrow x=15}\end{array}$

Number of student pre-ordered year book = $x=15$

Number of students paid full price = $24-x = 24-15 = 9$

Hence 15 students pre-ordered the year book and 9 students paid full price.