Problem 16 · 2004 AMC 8
Easy
Fractions, Decimals & Percents
mixture-fraction
Two 600 mL pitchers contain orange juice. One pitcher is 1/3 full and the other pitcher is 2/5 full. Water is added to fill each pitcher completely, then both pitchers are poured into one large container. What fraction of the mixture in the large container is orange juice?
Show answer
Answer: C — 11/30.
Show hints
Hint 1 of 2
The water is a red herring — adding water tops each pitcher to 600 mL but adds zero juice. So just track two numbers: how much juice total, and how much liquid total. Fraction = juice ÷ everything.
Still stuck? Show hint 2 →
Hint 2 of 2
The principle is track the part that matters, ignore the filler: the answer is (amount of OJ) / (total volume). Don't average the fractions 1/3 and 2/5 — that's the trap, since both pitchers end up the same final size only by coincidence of being equal.
Show solution
Approach: total juice over total volume
- Juice in: pitcher 1 has 600 × 1/3 = 200 mL, pitcher 2 has 600 × 2/5 = 240 mL. Total juice = 440 mL.
- Total liquid: both pitchers are filled, so 600 + 600 = 1200 mL.
- Fraction juice = 440 / 1200 = 11/30.
- Quick check: the two juice fractions 1/3 (≈ 0.33) and 2/5 (= 0.40) should blend to something between them, and 11/30 ≈ 0.367 sits right in the middle — here a plain average works only because the pitchers are equal-sized.
Another way — average the concentrations (equal pitchers only):
- Because both pitchers hold the same 600 mL, the mixture's juice fraction is the plain average of the two: (1/3 + 2/5) / 2.
- 1/3 + 2/5 = 5/15 + 6/15 = 11/15; halve it: 11/30.
- Caution: this shortcut only works when the containers are equal in size — otherwise you must weight by volume.
Mark:
· log in to save