Problem 23 · 2013 Math Kangaroo
Stretch
Ratios, Rates & Proportions
proportioncareful-counting
Peter has bought a rug that is 36 dm wide and 60 dm long. The rug is covered in squares that each contain either a sun or a moon, as shown in the picture. There are exactly nine squares along the width of the rug. The full length of the rug cannot be seen. How many moons would you see if you could see the entire rug?
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Answer: B — 67
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Hint 1 of 3
If 9 squares fit across the 36 dm width, work out how wide one square is.
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Hint 2 of 3
Use that square size to find how many squares fit along the 60 dm length.
Still stuck? Show hint 3 →
Hint 3 of 3
Multiply rows by columns for the total squares, then the sun/moon pattern splits them almost in half.
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Approach: find the grid size, then count one colour
- 36 dm ÷ 9 = 4 dm per square, so the length 60 dm holds 60 ÷ 4 = 15 squares.
- The rug is 9 × 15 = 135 squares in a checkerboard of suns and moons.
- The moons fall on the smaller of the two colour groups, giving 67 moons.
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