Question

An artist is using three different colors in a mosaic. The ratio of green to blue to yellow color tiles in the mosaic is 4:6:9. She has 42 blue tiles to use. How many green and yellow tiles does she need?

Answer 1

28 green and 63 yellow tiles.

Explanation:

The given ratio of green:blue:yellow is 4:6:9

Please remember that in ratios, the numbers are at the same place as that of the corresponding word that defines it.
For example, in the above question, green is 4, blue is 6, and yellow is 9.

It is also, given that there are 42 blue tiles to use which means 42 will replace the earlier 6 for the blue tiles.

Now, the new ratio will be, green:blue:yellow = ?:42:?
You can note that 4 & 9 have been replaced by ? because, in ratios and proportions, any change in any one of the ratios will have to change accordingly (multiplied or divided) for all other parts in the ratio.

So, we can see that 6 from the original ratio has been replaced by 42.

Then think of how much more (or less as the case maybe) is 42 from the original 6. We can easily find that 42 is 7 times of 6 because `7 xx 6 = 42`

Therefore, we have to multiply corresponding ratios of green (4) and yellow (9) with 7 to keep the ratios same.

Which is, green tiles should be = `4 xx 7 = 28` tiles
and, yellow tiles should be = `9 xx 7 = 63` tiles

So now, the new numbers of tiles in the same ratio of green (4):blue (6):yellow(9) is 28:42:63