Given:
A mother is now 2 and a half times old as her daughter Mary.
Four years ago the ratio of their ages was 3:1.
To find:
The present age of the mother.
Solution:
Let x be the present age Mary's mother and y be the present age of Mary.
A mother is now 2 and a half times old as her daughter Mary. So,
[tex]x=2\dfrac{1}{2}y[/tex]
[tex]\dfrac{x}{y}=\dfrac{2(2)+1}{2}[/tex]
[tex]\dfrac{x}{y}=\dfrac{5}{2}[/tex]
It means the ratio of their present age is 5:2. Let 5z be the present age of Mary's mother and 2z be the present age of Mary.
Four years ago the ratio of their ages was 3:1.
[tex]\dfrac{5z-4}{2z-4}=\dfrac{3}{1}[/tex]
[tex]1(5z-4)=3(2z-4)[/tex]
[tex]5z-4=6z-12[/tex]
[tex]-4+12=6z-5z[/tex]
[tex]8=z[/tex]
Now, the present age of the mother is:
[tex]5z=5(8)[/tex]
[tex]5z=40[/tex]
Therefore, the present age of the mother is 40 years.
