Today’s problem — free all day, every step. Every day has one.
Pens and pencils — after some pens are sold
A stationery shop had 200 more pencils than pens. After 100 pens were sold, the ratio of the number of pens to the number of pencils was 2 : 5. How many pencils were there?
Show the answerHide the answer
There were 500 pencils.
The pattern behind it: Constant part
The ratio changes, but one person's amount stays the same.
In this one. The pencils were never sold, so the gap between the two can only grow — it grows by exactly the 100 pens that left, which is why 200 + 100 = 300 is the value of the ratio's unit-gap.
How to spot it
A ratio changes and the question tells you only one person gained or lost an amount, while the other kept what they had.
Common mistake
Children keep the same number of shares for the person whose amount did not change. The amount stays the same, but the size of a share can differ between the two ratios.
Try one like it
Challenging Ali and Ben's savings — the ratio shifts The ratio of Ali's savings to Ben's savings was 3 : 5. After Ali saved another $24, the ratio became 9 : 10. How much did Ali have…The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.