Answer:
The three parts are 12,18 and 30
Explanation:
Let
x ----> the first part
y ----> the second part
z ----> the third part
we know that
[tex]x+y+z=60[/tex] -----> equation A
[tex]\frac{x}{y}=\frac{2}{3}[/tex]
[tex]x=\frac{2}{3}y[/tex] -----> equation B
[tex]\frac{y}{z}=\frac{3}{5}[/tex]
[tex]z=\frac{5}{3}y[/tex] ----> equation C
substitute the equation B and the equation C in equation A and solve for y
[tex]\frac{2}{3}y+y+\frac{5}{3}y=60[/tex]
[tex]\frac{10}{3}y=60[/tex]
[tex]y=60(3)/10[/tex]
[tex]y=18[/tex]
Find the value of x
[tex]x=\frac{2}{3}(18)=12[/tex]
Find the value of z
[tex]z=\frac{5}{3}(18)=30[/tex]
therefore
The three parts are 12,18 and 30
