Form Four Science of a school has n students. A farewell dinner is planned at the end of the year at a total cost of RM252. It is found that 6 of the students are unable to attend the dinner and because of this, each of those attending dinner will have to pay RM1 extra.
a) Show that n^2-6n-1512=0

Question

Form Four Science of a school has n students. A farewell dinner is planned at the end of the year at a total cost of RM252. It is found that 6 of the students are unable to attend the dinner and because of this, each of those attending dinner will have to pay RM1 extra.
a) Show that n^2-6n-1512=0

anonymous · Answer

@ganeshie8

britanyashton · Answer

can u clarify the meaning of RM? i assumed that meant room, but a room isn't a cost.

ganeshie8 · Answer

RM is just a currency unit like $ @britanyashton

ganeshie8 · Answer

There are $n$ students and the total cost is $252$, so each student has to contribute   $\dfrac{252}{n}$.

ganeshie8 · Answer

but 6 students are are unable to attend and that makes remaining $n-6$ students to pay RM1 more. So each student now contributes  $\dfrac{252}{n}+1$

ganeshie8 · Answer

$n-6$ students contribting $\dfrac{252}{n}+1$ each for a total of $RM 252$ : 

$$(n-6)\left(\frac{252}{n}+1\right) = 252$$

simplify ^

anonymous · Answer

$$252+n-1512-6=252$$

anonymous · Answer

@ganeshie8

ganeshie8 · Answer

$$(n-6)\left(\frac{252}{n}+1\right) = 252$$

$$(n-6)\left(252+n\right) = 252n$$

right ?

ganeshie8 · Answer

expand on left side and simplify

anonymous · Answer

$$252n+n^2-1512-6n=252n$$
$$n^2-6n-1512=0$$

anonymous · Answer

thnx @ganeshie8

ganeshie8 · Answer

looks good!