Multiple choice

One gallon of fuel mixture contains antifreeze in the ratio of $5$ parts fuel to one part antifreeze. To this is added half a gallon of mixture which is one third antifreeze and two thirds fuel. What is the ratio of fuel to antifreeze in the final mixture? (Grid your answer as a fraction: fuel/antifreeze)

  1. $\dfrac {3}{2}$
  2. $\dfrac {5}{2}$
  3. $\dfrac {7}{2}$
  4. $\dfrac {9}{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Mixture 1: 1 gallon (5/6 fuel, 1/6 antifreeze). Mixture 2: 0.5 gallon (2/3 fuel, 1/3 antifreeze) = 1/3 gallon fuel, 1/6 gallon antifreeze. Total fuel = 5/6 + 1/3 = 7/6. Total antifreeze = 1/6 + 1/6 = 2/6. Ratio = (7/6) / (2/6) = 7/2.

AI explanation

The initial 1 gallon mixture has 5 parts fuel and 1 part antifreeze, meaning it contains 5/6 gallons of fuel and 1/6 gallons of antifreeze. The added half gallon mixture is 1/3 antifreeze and 2/3 fuel by volume, contributing 1/3 gallons of fuel and 1/6 gallons of antifreeze. Combining these gives a total fuel volume of 5/6 plus 1/3, which is 7/6 gallons, and a total antifreeze volume of 1/6 plus 1/6, which is 2/6 gallons. The final ratio of fuel to antifreeze is (7/6) divided by (2/6), which equals 7/2.

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