Question Number 209065 by necx122 last updated on 01/Jul/24
$${The}\:{cost}\:{of}\:{maintaining}\:{a}\:{school}\:{is} \\ $$$${partly}\:{constant}\:{and}\:{partly}\:{varies}\:{as} \\ $$$${the}\:{number}\:{of}\:{students}.\:{With}\:\mathrm{50}\:{students} \\ $$$${the}\:{cost}\:{is}\:\$\mathrm{15705}\:{and}\:{with}\:\mathrm{40}\:{students} \\ $$$${the}\:{cost}\:{is}\:\$\mathrm{13305}.\:{If}\:{the}\:{fee}\:{per}\:{student} \\ $$$${is}\:\$\mathrm{360}.\mathrm{00},\:{what}\:{is}\:{the}\:{least}\:{number}\:{of} \\ $$$${students}\:{for}\:{which}\:{the}\:{school}\:{can}\:{be} \\ $$$${run}\:{without}\:{loss}? \\ $$
Answered by mr W last updated on 01/Jul/24
$${Cost}={a}+{bx}\:{with}\:{x}={number}\:{of}\:{students} \\ $$$$\mathrm{15705}={a}+\mathrm{50}{b} \\ $$$$\mathrm{13305}={a}+\mathrm{40}{b} \\ $$$$\Rightarrow{b}=\mathrm{240},\:{a}=\mathrm{3705} \\ $$$${Fee}=\mathrm{360}{x} \\ $$$${Fee}\geqslant{Cost} \\ $$$$\mathrm{360}{x}\geqslant\mathrm{3705}+\mathrm{240}{x} \\ $$$$\Rightarrow{x}\geqslant\mathrm{30}.\mathrm{9}\:\Rightarrow{at}\:{least}\:\mathrm{31}\:{students} \\ $$
Commented by necx122 last updated on 01/Jul/24
$${Thank}\:{you}\:{sir}. \\ $$