Problem 26 · 2022 Math Kangaroo
Stretch
Fractions, Decimals & Percents
proportionratio
A painter wants to mix 2 litres of blue paint with 3 litres of yellow to make 5 litres of green. By mistake he uses 3 litres of blue and 2 litres of yellow, making the wrong shade. What is the least amount of this green he must throw away so that, by adding only blue or yellow, the rest becomes exactly 5 litres of the correct shade?
Show answer
Answer: A — 5⁄3 litre
Show hints
Hint 1 of 2
The wrong mix is 3 blue : 2 yellow (5 L); correct green is 2 blue : 3 yellow. Compare the blue fractions.
Still stuck? Show hint 2 →
Hint 2 of 2
You may only ADD paint, so you must throw away enough wrong mix that the kept blue and yellow can still reach a 2:3 mix within 5 L.
Show solution
Approach: keep a portion that can be corrected by adding
- The wrong 5 L holds 3 L blue and 2 L yellow; correct green needs blue:yellow = 2:3 in 5 L (2 L blue, 3 L yellow).
- Keep a fraction k of the wrong mix: kept blue = 3k, yellow = 2k. Since you may only add, need 3k <= 2, so k <= 2/3.
- The minimum thrown away is 5(1 - 2/3) = 5/3 litre, so the answer is A.
Mark:
· log in to save