SOLUTION: Bob gave 4/5 of his pencils to Barb, then gave 2/3 of the remaining pencils to Bonnie. Bob ended up with 10 pencils left, how many did he start with?

Question 267120: Bob gave 4/5 of his pencils to Barb, then gave 2/3 of the remaining pencils to Bonnie. Bob ended up with 10 pencils left, how many did he start with?
Found 3 solutions by drk, richwmiller, CharlesG2:
Answer by drk(1908)   (Show Source): You can put this solution on YOUR website!
bob gave (4/5) P
bob left (1/5) p
---
bob gave (2/3)(1/5)p
bob left (1/3)(1/5)p = 10
---
(1/3)(1/5)p = 10
becomes
(1/15)p = 10
multiply by 15 to get
p = 150
---
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
(x-4x/5)=x/5
1/3*x/5=10
x/15=10
x=150
1/5*150=30 left after giving to Barb
30/3=10 left over
Answer by CharlesG2(834)   (Show Source): You can put this solution on YOUR website!
Bob gave 4/5 of his pencils to Barb, then gave 2/3 of the remaining pencils to Bonnie. Bob ended up with 10 pencils left, how many did he start with?
work backwards-->
10 pencils left is the 1/3 Bob did not give to Bonnie,
that makes 30 pencils before he gave 20 to Bonnie
the 30 pencils is the 1/5 Bob did not give to Barb,
that makes 150 pencils (30*5=150) Bob had to begin with
now work forward to check --> 150 pencils
less 120 to Barb --> (this is 4/5, 4/5 * 150 = 120)
now 30 pencils -->
less 20 to Bonnie --> (this is 2/3, 2/3 * 30 = 20)
left with 10 pencils

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