There are three colours of beads in abag.The ratio of red to yellow beads is 8:3The ratio of green to yellow beads is9:2.What fraction of the beads are green
Question
There are three colours of beads in a bag.
The ratio of red to yellow beads is 8:3.
The ratio of green to yellow beads is 9:2.
What fraction of the beads are green?
Solution
First, let's find a common ratio for yellow beads in both ratios.
The ratio of red to yellow beads is 8:3 and the ratio of green to yellow beads is 9:2.
To make the yellow beads the same in both ratios, we can multiply the first ratio by 2 and the second ratio by 3.
This gives us:
Red : Yellow = 82 : 32 = 16 : 6 Green : Yellow = 93 : 23 = 27 : 6
Now, the yellow beads are the same in both ratios, we can combine these ratios to get the ratio of red : yellow : green = 16 : 6 : 27
The total number of parts is 16 (red) + 6 (yellow) + 27 (green) = 49 parts
So, the fraction of the beads that are green is 27 (green) / 49 (total) = 27/49.
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