Help Needed With Sweets

[kuiperbelt]

A bag contains red and yellow sweets.

Some of the sweets are fizzy.
All the other sweets are bonbons.

The ratio of the number of red sweets to the number of yellow sweets is 4 : 3
The ratio of the number of red fizzy sweets to the number of red bonbons is 1 : 5
The ratio of the number of yellow fizzy sweets to the number of yellow bonbons is 4 : 5

What fraction of all the sweets are fizzy. Express your answer as a percentage.

[Gizmonster]

It doesn't matter how many sweets there are in total, but I've chosen an arbitrary amount for the ease of calculations.
Assume there are 4200 sweets in total
Therefore there are 2400 red (4200 x 4/7) and there are 1800 yellow (4200 x 3/7)
There are 400 red fizzy sweets (2400 x 1/6) and 2000 red bonbons (2400 x 5/6).
There are 800 yellow fizzy sweets (1800 x 4/9) and 1000 yellow bonbons (1800 x 5/9)
Total number of fizzy sweets is 400 + 800 = 1200
1200 of a total of 4200 sweets are fizzy:
1200/4200 x 100 = 28.57%

[bobbinwales]

i used 7x6x9=378 sweets
red to yellow 4:3 =216:162
so 216 red and 162 yellow
red fizzy to red bombon = 1:5 = 36 to 180
yellowfizzy to yellow bombon= 18x4:18x 5 =72 to 90

so fizzy total is 36 + 72=108
108 out of 378 simplify's to 2/7

Same as gizmonster (i think) but his explained it much better explained than me

[bobbinwales]

wish i done it his way with fractions, i allways made math's at school/night school harder than it should of been

[ZebuSanctuary]

Since the problem has already been solved, perhaps the following might be of use.

To satisfy the criteria has laid down in the question, the minimum number of sweets contained in the bag must be 21.

This equates to 12 red sweets and 9 yellow.

[bobbinwales]

Actually just realised that you can just do it by multiplying and adding fractions so 4/7 ×1/6
+
3/7×4/9
=2/21 + 4/21=6/21=3/7

[bobbinwales]

Last line typo.... 2/7.
My sums are better than my typing

[Barsel]

Don't worry about it, just eat them!

[smurfchops]

I agree Barsel. Yummy.

[kuiperbelt]

Barsel and smurf, please remember to brush your teeth afterwards!! ;-)