Question: Leighton and Jesse have a combined total of 36 CDs. After Leighton gives Jesse 40% of his CDs, Jesse has twice as many as Leighton. How many CDs did Leighton have initially?
Level: Year 8 question (Medium)
Solution: Trial & Error
Imagine the question as a real life scenario, and try out some numbers.
Firstly, we know we can’t have part of a CD, so when we consider 40% of Leighton’s pile, it must be out of a whole number of CDs. One such number would be 10. 40% of 10 is 4.
Therefore, Leighton, in this case, would hand over 4 CDs from his pile of 10, leaving him with 6 CDs. Since there are 36 CDs in total, Jesse would have 30 CDs. This doesn’t work because 30 is not double 6.
Try 20 for Leighton’s pile. 40% of 20 = 8. Therefore, Leighton would hand over 8 of his 20, leaving him with 12 CDs. This means that Jesse now has 24 CDs. 24 is double 12 which satisfies the condition (i.e. that Jesse now has double the amount of Leighton’s pile).
Make sure you finish the question off now. The final answer is that Leighton initially had 20 CDs.
How did you go with this question? What approach did you take to solve it?