Question

Ana şi Maria au împreună 760 lei. Să se afle câți bani are fiecare ştiind că 20% din suma Anei reprezintă 75% din suma Mariei.

Answer 1

 

$\displaystyle\bf\\ a+m=760\\\\20\%\times a=75\%\times m\\\text{---------------------}\\\\a+m=760\\\\\frac{20}{100}\times a=\frac{75}{100}\times m\\\\\text{---------------------}\\a+m=760\\20a=75m\\\text{---------------}\\a=760-m~~~~~~(Substitutie)\\\\20(760-m)=75m\\\\20\times760-20m=75m\\\\75m+20m=20\times760\\\\95m=15200\\\\m=\frac{15200}{95}\\\\\boxed{\bf~m=160~Lei~are~Maria}\\\\\text{\bf~Ne intoarcem la substitutie:}\\\\a=760-m=760-160\\\\\boxed{\bf~a=600~Lei~are~Ana}$