|
Question 1187556: Anton, Chris and Eddie had some tickets to sell for their school concert. After Anton sold 1/3 of his tickets, Chris sold 2/5 of his and Eddie sold 3/4 of his, they had an equal number of tickets left. If they sold tickets 225 altogether, how many tickets did each boy have left?
Answer by ikleyn(52798) (Show Source):
You can put this solution on YOUR website! .
Anton, Chris and Eddie had some tickets to sell for their school concert.
After Anton sold 1/3 of his tickets, Chris sold 2/5 of his and Eddie sold 3/4 of his,
they had an equal number of tickets left.
If they sold tickets 225 altogether, how many tickets did each boy have left?
~~~~~~~~~~~~~~
Let 3x be the number of tickets Anton had initially; then he sold x tickets and has 2x tickets left.
Let 5y be the number of tickets Chris had initially; then he sold 2y tickets and has 3y tickets left.
Let 4z be the number of tickets Eddie had initially; then he sold 3z tickets and has z tickets left.
From the condition, we have these equations
2x = z (1)
3y = z (2)
x + 2y + 3z = 225 (3)
From (1), exoress x = z/2 and substitute into equation (3); from (2), express y = z/3 and substitute into equation (3).
Then equation (3) takes the form
+ + 3z = 225.
Multiply both sides by 6 (all the terms); then simplify and find z
3z + 4z + 18z = 6*225
25z = 6*225
z = = 6*9 = 54.
So, according to the condition, each boy has 54 tickets left. ANSWER
Solved.
------------------
Notice that I chose my unknown variables in such a way to make my computations as simple as possible.
So if you want to learn something useful from my solution, learn about this my trick.
|
|
|
| |