The ratio of the number of apples to oranges to pears is 7:11:9. Tom ate 21 fruits. As a result, the ratio of the number of apples to oranges to pears became 2:3:3. How many fruits were left? .

• 27x = number of fruits initially
  8y = number of fruits after tom ate some
  
  27x - 21 = 8y
  putting x = 7 (by T&N)
  
  y = 21
  ans: 168
• 6 years agoHelpfull: Yes(3) No(25)
• what is T&N ??
• 6 years agoHelpfull: Yes(3) No(0)
• number of fruits initially 7x+11x+9x=27x
  
  
  number of fruits after tom ate some 2y+3y+3y=8y
  
  27x - 21 = 8y
  putting x = 7 (by T&N)
  
  y = 21
  ans: 168
• 6 years agoHelpfull: Yes(0) No(4)
• Since we won't be dealing in fractions here, the total number of fruits to begin with (
  B
  B
  ) must be a multiple of 7+11+9 = 27 and after Timmy pigs out, a multiple of 8 (
  A
  A
  ). That is because 7, 11, and 9 have no common factors, nor do 2 and 3.
  Let
  B
  B
  = 27
  b
  b
  and A = 8
  a
  a
  .
  27
  b
  b
  - 21 = 8
  a
  a
  We need to solve this Diophantine Equation in integers.
  b
  b
  =
  8a+21
  27
  
  8a+2127
  27 = 3 × 3 × 3, so 8a + 21 must be divisible by 3,
  21 is a multiple of 3, so 8
  a
  a
  must also be a multiple of 3.
  Therefore a must be a multiple of 3.
  Trying various multiples of 3, we find that the lowest value of a that makes this come out in integers is 21.
  (There are better ways of doing this, but in this case the slow method works because the numbers are small enough.)
  a
  a
  = 21, means there were 168 fruits left (8
  a
  a
  ):
  42 apples, 63 oranges, 63 pears (2
  a
  a
  , 3
  a
  a
  , 3
  a
  a
  )
  Adding the 21 fruits Timmy ate, makes 189 fruits
  189
  27
  
  18927
  = 7, so
  b
  b
  = 7
  49 apples, 77 oranges, 63 pears. (7
  b
  b
  , 11
  b
  b
  , 9
  b
• 6 years agoHelpfull: Yes(0) No(1)
• 27x = number of fruits initially
  8y = number of fruits after tom ate some
  
  27x - 21 = 8y
  putting x = 7 (21/3=7 )
  
  y = 21
  ans: 168
• 6 years agoHelpfull: Yes(0) No(0)