Another Maths problem 4 d day (Ratio)

[Symantec9]

Hi 2 all Maths shifu, another brain crackin' day...

 

Mother bought a total of 120 apples n oranges in d ratio of 3:5. After she gave away an equal nbr of ea type of fruits, d ratio of d nbr of apples to d nbr of oranges left is 3:8. How many apples does she have now?

 

 

 

 

 

 

 

 

 

 

 

Many thanks...

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Though answer is 18, got 2 it by guess n check method, wonder if there r other approaches?

[ImprezaGL]

original apple orange ratio 3:5

 

Orange: - - - - - 75

Apple: - - - 45

 

After giving away equal nbr x, orange apple rario 3:8

 

75

orange: x - - - - - - - -

Apple: x - - -

45

 

the 5 part of orange = 75 - 45 = 30

each part is = 30/5 = 6

 

so orange left 8x6 = 48

apple 3x6 = 18

[Carbon82]

Initial of 45 apples & 75 oranges (120 in total with ratio of apple to orange @3:5)

 

Now let assume X to be the numbers of each fruits to be given away. And after giving out X number of apples, and X number of oranges, the new apple to orange ratio will become 3:8 - or total of 11 parts. So the formulae should look like this:

 

45 - X = 3/11 (120 - 2X)

45 - X = 360/11 - 6/11X

X - 6/11X = 45 - 360/11

5/11X = 135/11

5X = 135

X = 27

 

Therefore, the number of apple she has now is 45 - 27 = 18.

[Symantec9]

wow bro imprezaGL, u'r very impressive, TQ for the enlightenment, greatly appreciated, struggling to find a better way 2 explain, thanks a million!

Edited June 11, 2008 by Symantec9

[Symantec9]

wow, another brilliant guy, thank u again, hv a great day

[Mivec9]

Initially, (5+3)units = 120

8 units = 120

1 unit = 15

Orange = 15 X 5 units = 75

Apple = 15 X 3 units = 45

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Let x be number gave away

75 - x = 8 Units (oranges)

45 - x = 3 Units (apples)

(75-45) = 5 Units

30 = 5 units

Hence, 1unit = 6

 

Apples: (3Units X 6) = 18 (ans)