Solution 1 (using two equations in two unknowns)
The condition says that
J - S = 5, (1) ("Jack is 5 years older than his sister")
J + S = 21. (2) ("The sum of their ages is 21")
Add the equations (1) and (2) (both sides). You will get
2J = 5 + 21 ---> 2J = 26 ---> J = 
= 13.
Thus you found Jack's age. He is 13 years old.
Then his sister is 13 - 5 = 8 years old.
Answer. Jack is is 13 years old. His sister is 8 years old.
Check. Please check yourself.
Solution 2 (using one equation)
Let J be Jack's age.
The Jack's sister age is (J-5) years.
The sum of their ages is 21, so
J + (J-5) = 21.
Simplify and solve for J.
2J - 5 = 21 ---> 2J = 21 + 5 = 26 ---> J = = 13.
We obtain the same result: Jack is 13 years old; his sister is 8 years old.
There is a bunch of lessons on age word problems
- Age problems and their solutions
- A fresh formulation of a traditional age problem
- Really intricate age word problem
- Selected age word problems from the archive
- OVERVIEW of lessons on age problems
in this site.
Read them and become an expert in solving age problems.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
It contains a lot of other word problems and many other interesting and useful things.
