<PRE><B>Question 890570</B>


the ratio of guavas and papayas in crate A is equal to 5:3.


the ratio of guavas and papayas in crate B is equal to 4:9.


a ratio of 5:3 means that, for every 8 pieces of fruit in crate A, 5 of them are guavas and 3 of them are papayas.


the total number of fruit in crate A therefore has to be a multiple of 8.


we can let x represent that multiple for the number of fruit in crate A.


if x is 1, then there are 5 guavas and 3 papayas for a total of 8.


if x is 100, then there are 500 guavas and 300 papayas for a total of 800.


the ratio will hold no matter the value of x.


5/3 is the same ratio as 500/300.


so that&#39;s where we start for crate A.


now they say that, if you take away half of the guavas from crate A, the total number of fruit in crate A will be equal to 308.


since we started with 5x guavas and took away half, then we are left with 5x/2 guavas.


the formula for crate A now becomes:


5x/2 + 3x = 308


if we solve this equation for x, we will find that x = 56.


this means that the original number of fruit in crate A had to be 5(56) + 3(56) = 280 + 168 = 448


if we took away half the guavas, this means that we took away 140 guavas.


we took those guavas and put them in crate B.


so 140 guavas were transferred from crate A to crate B.


now we know the ratio of guavas to papayas in crate B is 4:9.


this means that, for every 13 pieces of fruit in crate B, 4 of them are guavas and 9 of them are papayas.


this means that the total amount of fruit in crate B has to be a multiple of 13.


if we let y equal that multiple, then the total number of fruit in crate B is equal to 13y.


this means that the number of guavas in crate B is equal to 4y and the number of papayas in crate B is equal to 9y.


the ratio of guavas to papayas is 4/9.


we get the equation:


4y/9y = 4/9


now when we add 140 guavas to crate B, the total number of guavas becomes 4y + 140.


the total number of papayas stays the same at 9y.


the total number of fruit becomes 13y + 140


now instead of the ratio being 4/9, the ratio becomes 5/6.


so we get the equation:


(4y+140) / 9y = 5/6


we can use this equation to solve for y.


cross multiply to get:


6*(4y+140) = 9y*5


simplify to get:


24y + 840 = 45y


subtract 24y from both sides of the equation to get:


840 = 21y


divide both sides of this equation by 21 to get:


y = 40


now let&#39;s see what we have.


the original ratio is 4/9 and is composed of 4y + 9y = 13y


when y = 40, this becomes 4(40) + 9(40) = 13(40) which becomes 160 + 360 = 520 which becomes 520 = 520.


this means that we originally had 520 pieces of fruit in crate B and that 160 of them were guavas and 360 of them were papayas.


if we add 140 to that, then the pieces of fruit in crate B goes from 520 to 660.


but now we have a new ratio of 5/6.


this means that for every 11 pieces of fruit in crate B, 5 of them are guavas and 6 of them are papayas.


so the total number of fruit in crate B will now be a multiple of 11.


if we let z equal that multiple, then we get:


5z + 6z = 11z = 660


solve for z to get z = 60


5z + 6z becomes 5(60) + 6(60) = 11(60) which becomes 300 + 360 = 660 which becomes 660 = 660.


this confirms that the multiple of z = 60 is correct.


we originally had 160 guavas and 360 papayas in crate B.


we now have 300 guavas and 360 papayas in crate B.


the number of guavas in crate B grew by 140.


the numbers check out and we now have all answers to the problem.


the questions to the problem were:


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?


the answer to question A is that 140 guavas were transferred from crate A to crate B.


the answer to question B is that the number of fruit in crate B after the transfer is 660.





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