Question 969376: Darren had 35 more pencils than Jimmy. Darren gave 60%of his pencils to Jimmy. Jimmy in return gave 20% of his pencils to Darren. In the end, Jimmy had 21 more pencils than Darren. How many pencils did Jimmy have at first?
Found 2 solutions by MathTherapy, Theo:
Answer by MathTherapy(10556)   (Show Source):
You can put this solution on YOUR website!
Darren had 35 more pencils than Jimmy. Darren gave 60%of his pencils to Jimmy. Jimmy in return gave 20% of his pencils to Darren. In the end, Jimmy had 21 more pencils than Darren. How many pencils did Jimmy have at first?
Initial number Jimmy had: 
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! you are looking for the missing number.
call that number x.
x represents the number of pencils that jimmy has to start with.
my worksheet is shown below.
step 1 takes 60% of what darren has to start with and gives it to jimmy.
darren is left with 40% of what darren had to start with.
jimmy is l4eft with 60% of what darren had to start with plus what jimmy had to start with.
darren started with x + 35.
after step 1 darren was left with 40% of x + 35.
jimmy started with x.
after step 1 jimmy had x + 60% of x + 35.
step 2 subtract 20% of what jimmy had after step 1 and gives it to darren.
jimmy started step 2 with 1.6x + 21.
jimmy is left with 1.6x + 21 minus .2 * (1.6x + 21) after step 2 which is equal to 1.28x + 16.8.
darren started step 2 with .4x + 14.
darren added .2 * (1.6x + 21) to that.
darren is left with .72x + 18.3 after step 2.
step 3 says that, after all is said and done, darren is left with 21 more pencils than jimmy.
since jimmy has 1.28x + 16.8 pencils, and darren has .72x 18.2 pencils, this means that:
1.28x + 16.8 = .72x + 18i.2 + 21.
this statement says that what jimmy has is equal to what darren has plus 21.
solve for x in step 3 and yoju get x = 40.
that must be what jimmy had to start with.
after that is verification.
darren starts with 75 and jimmy starts with 40.
after step 1, darren has 30 and jimmy had 85.
after step 2, darren has 47 and jimmy has 68.
after step 3, it is clear that 68 pencils is 21 more pencils than 47.
my worksheet is shown below:
|
|
|
