SOLUTION: Dear Sir I would be glad if you can help me to resolve the below problems that has been bothering me for awhile. Thanks Jackie King e-mail address; smsltd@starhub.net.sg 1)

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Question 178909: Dear Sir
I would be glad if you can help me to resolve the below problems that has been bothering me for awhile.
Thanks Jackie King
e-mail address; smsltd@starhub.net.sg
1) Jane had 156 red and yellow beads in the ratio 7:6. After she gave away an equal number of each type of bead, the number of red and yellow beads left was in the ratio 7:3.
(a) Did the fraction of the red beads that Jane had increases, decreases, or remain the same?
(b) How many beads did she give away altogether?

2) In Mariam’s aquarium there are swordtails and guppies, 25% of the fishes are swordtails. She then buys an equal number of swordtails and puts them into the aquarium.
(a) Will the percentage of fishes in the aquarium which are guppies increases, decrease or remain the same?
(b) What percentage of the fishes will be guppies?
My queries in the above the two questions are:
In question 1 (a) does the ‘fraction’ asked refers to the new base after “she gave away an equal number of each type of bead “ or referring the same base before giving away. If the answer is related to the new base then my question is how we can compare two fractions coming from different wholes; I could not find any mathematical meaning in this situation.
Similar query in question two in which I wonder which ‘whole’ the question refers to; before or after. In addition, the quantity “an equal number of swordtails” refers to the same amount of 25% of the fishes.
Lastly, what principles do the examiner what to test in the above two questions.
I would appreciate very much if you would provide me the method how you would work the solutions to the above questions.
Furthermore, what happen if we keep increasing or increasing the “equal amount to put in or taken away”? Is there some kind of relationship that we can deduce from these two problems?

Answer by ankor@dixie-net.com(12704) (Show Source):
You can put this solution on YOUR website!
1) Jane had 156 red and yellow beads in the ratio 7:6. After she gave away an equal number of each type of bead, the number of red and yellow beads left was in the ratio 7:3.
:
(a) Did the fraction of the red beads that Jane had increases, decreases, or remain the same?
:
Try it and see, we know that 156/13 = 12 therefore there are:
7*12 = 84 red
6*12 = 72 yellow
decimal equiv of red beads 84/156 = .538
Give away two of each, reducing the total to 152
decimal equiv of red beads: 82/152 = .539, fraction of red beads has increased
:
:
(b) How many beads did she give away altogether?
;
let amt of each given away = x
=
Cross multiply
3(84-x) = 7(72-x)
252 - 3x = 504 - 7x
-3x + 7x = 504 - 252
4x = 252
x =
x = 63 ea given away
:
Check this: = =
:
:
2) In Mariam’s aquarium there are swordtails and guppies, 25% of the fishes are swordtails. She then buys an equal number of swordtails and puts them into the aquarium.
:
(a) Will the percentage of fishes in the aquarium which are guppies increases, decrease or remain the same?
:
Lets say there are 25 swords in the tank which contains 100 fish (75 are gups)
then, the decimal amt of guppies will be .75 (75%)
Add 25 more swords, total fish = 125, no. of guppies remain at 75 so we have:
= .60 (60%) so it decreases
(b) What percentage of the fishes will be guppies? 60%
:
:
Hopefully I straightened this out. Let me know Carl