Answer:
The present age of the mother is 30 years
Step-by-step explanation:
Let
x ---> Sara's age (the mother)
y ---> Billy's age (the son)
z ---> Jane's age (the daughter)
we know that
Billy is five times as old as Jane
so
[tex]y=5z[/tex] ----> equation A
Their mother is now three times as old as Billy
[tex]x=3y[/tex] ----> equation B
Their mother in 2 years she will be eight times as old as Jane
so
[tex]x+2=8(z+2)[/tex] ---> equation C
substitute equation A in equation B
[tex]x=3(5z)[/tex]
[tex]x=15z[/tex] ----> equation D
substitute equation D in equation C
[tex]15z+2=8(z+2)[/tex]
solve for z
[tex]15z+2=8z+16\\15z-8z=16-2\\7z=14\\z=2[/tex]
Find the value of x
[tex]x=15(2)=30[/tex]
therefore
The present age of the mother is 30 years
