Question Number 66767 by John Kaloki Musau last updated on 19/Aug/19
$${In}\:{a}\:{school}\:{there}\:{are}\:\mathrm{30}\:{more}\:{boys} \\ $$$${than}\:{girls}.\:{One}-{quarter}\:{of}\:{the}\:{boys} \\ $$$${and}\:{two}-{thirds}\:{of}\:{the}\:{girls}\:{are}\:{boarders}. \\ $$$${If}\:{there}\:{are}\:\mathrm{255}\:{boarders},\:{find}\:{the} \\ $$$${number}\:{of}\:{students}\:{in}\:{the}\:{school}. \\ $$
Commented by Prithwish sen last updated on 19/Aug/19
$$\mathrm{let}\:\mathrm{no}.\:\mathrm{of}\:\mathrm{girls}\:=\:\mathrm{x} \\ $$$$\mathrm{No}.\:\mathrm{of}\:\mathrm{boys}\:=\:\mathrm{x}+\mathrm{30} \\ $$$$\therefore\:\frac{\mathrm{x}+\mathrm{30}}{\mathrm{4}}\:+\frac{\mathrm{2x}}{\mathrm{3}}\:=\:\mathrm{255} \\ $$$$\mathrm{3x}+\mathrm{90}+\mathrm{8x}\:=\:\mathrm{3060} \\ $$$$\mathrm{11x}=\mathrm{2970} \\ $$$$\mathrm{x}=\mathrm{270}\:\:\therefore\:\mathrm{No}\:\mathrm{of}\:\mathrm{students}\:=\:\mathrm{2}×\mathrm{270}+\mathrm{30}=\mathrm{570} \\ $$
Commented by John Kaloki Musau last updated on 20/Aug/19
wow!thanks a lot