El señor Pablo debe hacer el pago de servicios. Si gasta la mitad de su dinero en la luz, con la tercera parte de lo que le queda paga el gas y el agua lo paga con los ⅚ de lo que le quedó. ¿Con cuánto dinero contaba al inicio si después de pagar todo aún le quedó 24 soles?

Mr. Pablo must make payment for services. If he spends half of his money on electricity, with the third part of what he has left he pays for the gas and the water with the ⅚ of what he has left. How much money did he have at the beginning if after paying everything he still had 24 soles left?

Let

x ----> amount of money at the beginning

we know that

1) He spends half of his money on electricity

so

amount spent is----> [tex]\frac{1}{2}x[/tex]

remaining money ---> [tex]x-\frac{1}{2}x=\frac{1}{2}x[/tex]

2) With the third part of what he has left he pays for the gas

amount spent is----> [tex](\frac{1}{3})\frac{1}{2}x=\frac{1}{6}x[/tex]

remaining money ---> [tex]\frac{1}{2}x-\frac{1}{6}x=\frac{2}{6}x= \frac{1}{3}x[/tex]

3) He pays for the water with the ⅚ of what he has left

amount spent is----> [tex](\frac{5}{6})\frac{1}{3}x=\frac{5}{18}x[/tex]

remaining money ---> [tex]\frac{1}{3}x-\frac{5}{18}x=\frac{1}{18}x[/tex]

4) The remaining money is 24 soles

so

[tex]\frac{1}{18}x=24[/tex]

solve for x

[tex]x=18(24)=432\ soles[/tex]