Problem 12 · 2017 Math Kangaroo
Stretch
Arithmetic & Operations
total-then-dividecareful-counting
Lisa has several sheets of construction paper, of two kinds (shown). She wants to make 7 identical crowns, and for that she cuts out the necessary parts. What is the minimum number of sheets of construction paper that she has to cut up?
Show answer
Answer: B — 9
Show hints
Hint 1 of 2
First count exactly what one crown is made of: how many dots, crosses, and bars.
Still stuck? Show hint 2 →
Hint 2 of 2
Only the first kind of sheet has bars, and you need one bar per crown; start by getting enough bars, then top up the dots.
Show solution
Approach: cover the scarce part first (bars), then make up the dots
- Each crown needs 4 dots, 1 cross, and 1 bar, so 7 crowns need 28 dots, 7 crosses, and 7 bars.
- Only the first kind of sheet has bars (2 bars, plus 1 dot and 1 cross each); to get 7 bars she needs 4 of these sheets, giving 8 bars, 4 dots, and 4 crosses.
- She still needs 28 - 4 = 24 more dots; the second kind of sheet has 5 dots (and 3 crosses) each, so 5 of them give 25 dots — enough, and plenty of crosses.
- Total = 4 + 5 = 9 sheets.
Mark:
· log in to save