Sisters and brothers
Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?
Age
7 to 11
Challenge level
Problem
Cassandra, David and Lachlan are brothers and sister.
They range in age between $1$ year and $14$ years.
Can you figure out their exact ages from the clues?
Lachlan's age and David's age added together is $10$ years.
Cassandra's age and Lachlan's age added together is $15$ years.
David's age and Cassandra's age added together is $19$ years.
This problem was made up and sent in by Cassandra from Cambridge in the UK. Thank you Cassandra!
Getting Started
What could you try to start with?
What does that tell you about the ages of the other children?
What do you know about David's age compared with Lachlan's age?
What does that tell you about the ages of the other children?
What do you know about David's age compared with Lachlan's age?
Student Solutions
We received this solution from someone who didn't give their name:
Lachlan is $3$
David is $7$
C is $12$
I first looked at the ones with Cassandra in and found the difference, which was $4$, so that means David and Lachlan's ages have a difference of $4$. I then worked out that $7$ and $3$ have a difference of $4$ and make $10$. So, either David is $7$ and Lachlan is $3$ or the other way round.
When I took $7$ from $19$ to get Cassandra's age, that made $12$ and it also made $12$ if I took $3$ from $15$, so it must be that way round.
Teachers' Resources
Why do this problem?
This problem encourages children to use number operations and
either trial and improvement, or a systematic approach to reach a
solution. It would be interesting to share the different ways they
use jottings to help during the problem-solving
process. The problem could be used to introduce
algebraic notation.
Key questions
What could you try to start with?
What does that tell you about the ages of the other
children?
What do you know about David's age compared with Lachlan's
age?
Possible extension
Learners could make up another similar problem for a friend to
solve.
Possible support
You could ask questions such as 'what if Lachlan is one year
old?' and encourage children to work out the ages of Cassandra and
David to see whether all the information holds true. If not, invite
learners to suggest what to try next.