SOLUTION: Mr Tong has some guavas and papayas in two crates. In crate A, the number of guavas and papayas are in the ratio of 5:3. In crate B, the number of guavas is 4/9 the number of papa
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Question 890566: Mr Tong has some guavas and papayas in two crates. In crate A, the number of guavas and papayas are in the ratio of 5:3. In crate B, the number of guavas is 4/9 the number of papayas. Mr Tong transfers half of the guavas from crate A to crate B. The number of fruits in crate A becomes 308 and the ratio of the number of guavas to the number of papayas in crate B becomes 5:6.
(a) How many guavas have been transferred from crate A to crate B?
(b) What is the number of fruits in crate B after the transfer? Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! Let = number of guavas in crate A
Let = number of papayas in crate A
Let = number of guavas in crate B
Let = number of papayas in crate B
----------------------------------------
(1)
(2)
(2)
-------------------------
After transfer: guavas in crate A guavas in crate B
------------------------------------ fruits in crate A
(3)
-------------------------------
(4)
-------------------------------
(3)
and, from (1):
(1)
(1)
(1)
By substitution:
(3)
(3)
(3)
(3)
(3)
---------------------
(2)
(2)
And, after transfer:
(4)
(4)
(4)
(4)
Substitute (2) into (4)
(4)
(4)
(4)
(4)
(4)
--------------------
-------------------
(a) 140 guavas were transferred to crate B
-------------------
(4)
(4)
(4)
(4)
(4)
---------------------
After the transfer,
--------------------------------
(b) There are 660 fruits in crate B
check:
(1)
(1)
(1)
(1)
and
(3)
(3)
(3)
OK
