Let [tex]x[/tex] represent Mandy's age and [tex]y[/tex] represent Sandy's.
From the first statement we have:
[tex]5x=2y[/tex]
From the second statement we have:
[tex]2*(x + 8) = 1*(y + 8)[/tex]
So we need to solve this system of equations:
[tex]\left \{ {{5x=2y} \atop {2(x+8)=y+8}} \right.[/tex]
Express [tex]y[/tex] from first equation equation:
[tex]2y=5x[/tex]
[tex]y=\frac{5}{2}x[/tex]
Replace found value in second equation and solve the resulting equation:
[tex]2(x+8)=\frac{5}{2}x+8[/tex]
[tex]2x+16=\frac{5}{2}x+8[/tex]
[tex]2x-\frac{5}{2}x=8-16[/tex]
[tex]-\frac{1}{2}x=-8[/tex]
[tex]\frac{1}{2}x=8[/tex]
[tex]x=8*2=16[/tex]
Replace found value in first equation and solve the resulting equation:
[tex]5*16=2y[/tex]
[tex]2y=80[/tex]
[tex]y=40[/tex]
So, Mandy is 16 years old and Sandy is 40 years old. The difference between their ages is 40 - 16 = 24 years.
