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Question Number 113097 by nimnim last updated on 11/Sep/20

If 4 women earn as much as 9 boys; 4 men as much as 15 boys; 27 girls as much as 20 women, how many girls will earn the same amount as 24 men?

$$\mathrm{If}\:\mathrm{4}\:\mathrm{women}\:\mathrm{earn}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as}\:\mathrm{9}\:\mathrm{boys};\:\mathrm{4}\:\mathrm{men}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as} \\ $$$$\mathrm{15}\:\mathrm{boys};\:\mathrm{27}\:\mathrm{girls}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as}\:\mathrm{20}\:\mathrm{women},\:\mathrm{how}\:\mathrm{many}\:\mathrm{girls} \\ $$$$\mathrm{will}\:\mathrm{earn}\:\mathrm{the}\:\mathrm{same}\:\mathrm{amount}\:\mathrm{as}\:\mathrm{24}\:\mathrm{men}? \\ $$

Answered by 1549442205PVT last updated on 11/Sep/20

4 men as much as 15 boys ⇒24 men as much as 15×6=90 boys 4 women as much as 9 boys ⇒20 women as much as 9×5=45 boys since 27 girls as much as 20 women , 27 girls as much as 45 boys(1) 24 men as much as 90 boys(2) From (1)(2) infer 54 girls will earn the same amount as 24 men Answer is 54 girls equal 24 men about food

$$\mathrm{4}\:\mathrm{men}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as}\:\mathrm{15}\:\mathrm{boys} \\ $$$$\Rightarrow\mathrm{24}\:\mathrm{men}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as}\:\mathrm{15}×\mathrm{6}=\mathrm{90}\:\mathrm{boys} \\ $$$$\mathrm{4}\:\mathrm{women}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as}\:\mathrm{9}\:\mathrm{boys} \\ $$$$\Rightarrow\mathrm{20}\:\mathrm{women}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as}\:\mathrm{9}×\mathrm{5}=\mathrm{45}\:\mathrm{boys} \\ $$$$\:\mathrm{since}\:\mathrm{27}\:\mathrm{girls}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as}\:\mathrm{20}\:\mathrm{women}\:, \\ $$$$\mathrm{27}\:\mathrm{girls}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as}\:\mathrm{45}\:\mathrm{boys}\left(\mathrm{1}\right) \\ $$$$\mathrm{24}\:\mathrm{men}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as}\:\mathrm{90}\:\mathrm{boys}\left(\mathrm{2}\right) \\ $$$$\mathrm{From}\:\left(\mathrm{1}\right)\left(\mathrm{2}\right)\:\mathrm{infer}\:\mathrm{54}\:\mathrm{girls}\:\mathrm{will}\:\mathrm{earn} \\ $$$$\mathrm{the}\:\mathrm{same}\:\:\mathrm{amount}\:\mathrm{as}\:\mathrm{24}\:\mathrm{men} \\ $$$$\mathrm{Answer}\:\mathrm{is}\:\mathrm{54}\:\mathrm{girls}\:\mathrm{equal}\:\mathrm{24}\:\mathrm{men} \\ $$$$\mathrm{about}\:\mathrm{food} \\ $$

Commented by nimnim last updated on 11/Sep/20

Thank you Sir.

$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{Sir}. \\ $$

Commented by 1549442205PVT last updated on 12/Sep/20

You are welcome.

$$\mathrm{You}\:\mathrm{are}\:\mathrm{welcome}. \\ $$

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