Today’s problem — free all day, every step. Every day has one.
Three flowerbeds — the overlaps
Three circular flowerbeds X, Y and Z in a park overlap one another. The combined area of Y and Z is of the area of X. Where X overlaps Y, the overlapping part is of Y's area. Where X overlaps Z, the overlapping part is of Z's area. Altogether, the shaded (overlapping) part of X makes up of X's area. Find X : Y : Z.
Show the answerHide the answer
See all 7 steps
MathBrush is being tested with a few parent groups, and every solution on the site is open to them — one household, all children. If you were given a code, it goes in once and this device remembers it.
I have a code → See a free one like it
65 worked examples are free without a code, two from every pattern. No account, either way.
The pattern behind it: Repeated identity
One length or count, described two ways in the same question.
In this one. Each overlap is the same physical patch whether measured as part of Y or Z or as part of X, so the two overlap fractions can be added and equated to the shaded fraction of X.
How to spot it
A shape or count is described from two viewpoints in the same question, such as one edge measured as a number of long pieces and again as a number of short pieces.
Common mistake
Children treat the two descriptions as separate quantities and add them. Both describe the same quantity, so the two must be equal.
Try one like it
Standard Water — poured into a second container A rectangular tank measures 30 cm by 20 cm by 25 cm. It is 3/5 full of water. All the water is poured into a second rectangular co…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.