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Ymorist [56]
3 years ago
6

Pre-orders for the yearbook cost $38 each and full price cost $45 each. If 24 students in Mr. Hillman's class purchased yearbook

s for a total of $975, how many students pre-ordered and how many paid full price?
Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
8 0

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

<u>Solution: </u>

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.

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