Question Number 209602 by peter frank last updated on 16/Jul/24
Answered by som(math1967) last updated on 16/Jul/24
$$\:{let}\:{number}={x} \\ $$$$\:\frac{\mathrm{120}{x}}{\mathrm{100}}\:−\frac{\mathrm{85}{x}}{\mathrm{100}}=\mathrm{14} \\ $$$$\:\frac{\mathrm{35}{x}}{\mathrm{100}}=\mathrm{14} \\ $$$$\Rightarrow{x}=\frac{\mathrm{14}×\mathrm{100}}{\mathrm{35}}=\mathrm{40} \\ $$
Commented by peter frank last updated on 18/Jul/24
$$\mathrm{thank}\:\mathrm{you} \\ $$
Answered by som(math1967) last updated on 16/Jul/24
$${let}\:{no}\:{of}\:{books}={x} \\ $$$$\:\frac{\mathrm{3600}}{{x}}\:−\frac{\mathrm{3600}}{{x}+\mathrm{6}}=\mathrm{50} \\ $$$$\Rightarrow\frac{\mathrm{3600}\left({x}+\mathrm{6}−{x}\right)}{{x}^{\mathrm{2}} +\mathrm{6}{x}}=\mathrm{50} \\ $$$$\Rightarrow\mathrm{72}×\mathrm{6}={x}^{\mathrm{2}} +\mathrm{6}{x} \\ $$$$\Rightarrow{x}^{\mathrm{2}} +\mathrm{6}{x}−\mathrm{72}×\mathrm{6}=\mathrm{0} \\ $$$$\Rightarrow{x}^{\mathrm{2}} +\left(\mathrm{24}−\mathrm{18}\right){x}−\mathrm{72}×\mathrm{6}=\mathrm{0} \\ $$$$\Rightarrow\left({x}+\mathrm{24}\right)\left({x}−\mathrm{18}\right)=\mathrm{0} \\ $$$$\:{x}=\mathrm{18}\: \\ $$
Commented by peter frank last updated on 18/Jul/24
$$\mathrm{thank}\:\mathrm{you} \\ $$