SOLUTION: Derek had 5/6 as many lollipops as Justin. When Justin gave half of his lollipops to Derek, he had 60 fewer lollipops than his friend. How many lollipops did Justin have at first?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Derek had 5/6 as many lollipops as Justin. When Justin gave half of his lollipops to Derek, he had 60 fewer lollipops than his friend. How many lollipops did Justin have at first?      Log On


   

Question 1194888: Derek had 5/6 as many lollipops as Justin. When Justin gave half of his lollipops to Derek, he had 60 fewer lollipops than his friend. How many lollipops did Justin have at first?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Derek had 5/6 as many lollipops as Justin.
When Justin gave half of his lollipops to Derek, he had 60 fewer lollipops than his friend. How many lollipops did Justin have at first?
:
let j = original no. of lollipops that Justin had
then
5%2F6j = original no. that Derek had
:
"When Justin gave half of his lollipops to Derek, he had 60 fewer lollipops than his friend.
1%2F2j = 5%2F6j + 1%2F2%7Dj+-+60%0D%0Acommon+denominator+is+6%0D%0A%7B%7B%7B3%2F6j = 5%2F6j + 3%2F6%7Dj+-+60%0D%0A%7B%7B%7B3%2F6j = 8%2F6j - 60
get rid of the fractions, multiply by 6, cancel the fractions
3j = 8j - 6(60)
3j - 8j = -360
-5j - -360
j = -360/-5
j = 72 lollipops, Justin had at first
:
:
Check this, (5/6)72 = 60 lollipops Derek had at first
half of 72 is 36, therefore
36 = 60 + 36 - 60