SOLUTION: Mary is 7 years younger than Jane. In four years'time, Mary will be one year older than half of Jane's age at that time. How old are Mary and Jane now?

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Mary is 7 years younger than Jane. In four years'time, Mary will be one year older than half of Jane's age at that time. How old are Mary and Jane now?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 623183: Mary is 7 years younger than Jane. In four years'time, Mary will be one year older than half of Jane's age at that time. How old are Mary and Jane now?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let M = Mary's present age and J = Jane's present age.
1) M+=+J-7 "Mary is 7 years younger than Jane."
2) M%2B4+=+%281%2F2%29%28J%2B4%29%2B1 "In 4 year's time, Mary will be one year older than half of Jane's age at that time."
Substitute M from equation 1) into equation 2).
3) %28J-7%29%2B4+=+%281%2F2%29%28J%2B4%29%2B1 Simplify and solve for J.
3a) J-3+=+%281%2F2%29J%2B3 Multiply through by 2 to clear the fraction.
3b) 2J-6+=+J%2B6 Subtract J from both sides.
3c) J-6+=+6 Add 6 to both sides.
3d) J+=+12 Jane is 12 years old.
2a) M+=+12-7
2b) M+=+5 Mary is 5 year old.