Question

Mr. Wilson works at a fruit packing factory. He has to pack 37.5 pounds of grapes. He has packed 0.5 of the total pounds of grapes into boxes with 2 1/12 pounds of grapes in each. How many boxes has Mr. Wilson packed?

Answer 1

9 boxes have been packed

Explanation:

Here we have a problem which has mixed representations of numbers decimals and fractions. Either convert all fractions to decimals or all decimals to fractions to solve

Though both will give the same result when rounded, in this case it is easier to convert everything to fractions because 1/12 cannot be represented accurately

• Convert 37.5 to a mixed fraction
  37.5 = 37 + 0.5 = 37 + 1/2 = 37 1/2
  
• Convert mixed fraction 37 1/2 to improper fraction
  37 1/2 = (37 x 2 + 1)/2 = 75/2
  
• Convert 0.5 to fraction
  0.5 = 1/2
  
• He has packed 1/2 of 75/2 pounds
  => 1/2 x 75/2 = 75/4 pounds packed
  
• Each box contains 2 1/12 pounds
  2 1/12 = (2 x 12 + 1)/12 = 25/12 pounds
  
• Number of boxes packed
  = Pounds packed ÷ pounds per box
  = 75/4 ÷ 25/12
  
  When fraction is a divisor, flip the fraction and multiply by dividend
  ==> 75/4 x 12/25
  = (75 x 12)/(4 x 25)
  = 900/100
  = 9 boxes

Verify:

• If half the total quantity can be packed in 9 boxes, it will take 18 boxes to pack the whole stuff
• Each box can hold 25/12 pounds
• 18 boxes can hold 18 x 25/12 = 18/12 x 25 = 3/2 x 25 = 75/2 = 37.5 lbs
  Hence checks out