Files and pens — the cost of 1 pen
The total cost of 2 identical files and 1 pen is $19.05. The total cost of 3 such files and 5 such pens is $44.50. Find the cost of 1 pen.
Sent in by a reader. Send me the one you are stuck on →
The pattern behind it: The equal concept
The question tells you a part of one pile equals a part of another.
In this one. Multiply each purchase until the item you do not want appears the same number of times in both — then the difference between the two totals is made of the wanted item alone.
How to spot it
Two different groups each get their own fraction or percentage, and the question links them with 'the same as', 'twice as many as', or a shared cost across different units.
Common mistake
Children compare the two fractions without first relating them to a common whole. A smaller fraction of a larger group can be bigger than a larger fraction of a smaller group.
Try one like it
Standard Marbles — red and blue boxes, matching fractions 3/5 of a box of red marbles equals 2/3 of a box of blue marbles. The box of red marbles contains 30 marbles. How many blue marbles…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.