Question

14. Divida 150 em partes inversamente proporcionais a 2 e 3.

Answer 1

x+y=150
x/1/2=y/1/3=r

x+y
2x=3y=r

2x/2=r/2
x=r/2
x=30/2
x=15

3y/3=r/3
y=r/3
y=30/3
y=10

x+y = 150
r/2+ r/3=150
3r/6+2r/6=150
5r=150
r=30

Answer 2

             A + B = 150
            
             1/2 e 1/3  <-- inversos de 2 e 3
             1/2 + 1/3 = -----mmc(2,3)=6
              3/6 + 2/6 =5/6         

             Então vamos dividir 150 por 5/6:
                        150 : 5/6 = 150 . 6/5 = 180

         Logo:
                  $\frac{A}{ \frac{1}{2} } = 2A = 180 ---\ \textgreater \ A = 180 : 2 = 90$

                  $\frac{B}{ \frac{1}{3} } = 3B = 180 --\ \textgreater \ B = 180 : 3 --\ \textgreater \ B = 60$