Question

How do I solve this Grade 9 Ratio question?

A bag contains green, red and blue balls. There are 36 balls in the bag, the ratio of green balls to red balls is 3:2 and the ratio of red balls to blue balls is 1:2.

• What is the ratio of green balls to blue balls?

• How many blue balls are in the bag?

• If another four red balls are added to the bag, what is the ratio of red balls to green balls?

YOUR HELP IS GREATLY APPRECIATED!

Answer 1

See below

Explanation:

The approach I took was:

Given `G/R=3/2` and `R/B=1/2`

`G/cancelRxxcancelR/B= 3/2xx1/2= 3/4= G/B`

`G/B=3/4`

Now for the next part, I need a ratio of blue out of the total:
`B/T= 4/(4+3+2)= x/36`

`9x=144`

`x=16`

There's 16 total blue balls

`R/T= 2/(4+3+2)=x/36`

`9x=72`

`x=8`

There's 8 total Red balls

`G/T=3/(4+3+2)=x/36`

`9x=108`

`x=12`

There's 12 total Green balls

So if 4 Red balls were added:

`12/12=1`
The new ratio of `R/G= 1`

Answer 2

1. 3:4
2. 16 (blue) balls
3. 3:4

Explanation:

Green to red balls: `3:2` or 3 green every 2 red. We can write this as `(3" green")/(2" red")`
Red to blue balls: `1:2` or 1 red every 2 blue (2 blue every 1 red). We can write this as either `(1" red")/(2" blue")` or `(2" blue")/(1" red")`

This also means that if you had 3 green balls, you would have 2 red balls, and 4 blue balls. See the below conversion for explanation:
`(3" green")/(2\cancel{" red"})xx(1\cancel{" red"})/(2" blue")=(3xx1" green")/(2xx2" blue")=(3" green")/(4" blue")`

So your answer for the first question is `\color{red}{3:4}`

Your overall ratio of green-red-blue is `3:2:4`. Let's set a random value x to compare:
`3x` green to `2x` red to `4x` blue. We know that the total ball amount is 36, so `3x+2x+4x=36`

Let's simplify that to find `x` (then we can calculate how many balls of each color there are, by plugging in the `x`):
`9x=36`
`x=36\div9=4`

So your ball count is:
Green `3x=3(4)=12` balls
Red `2x=2(4)=8` balls
Blue `4x=4(4)=16` balls

Your answer for the second question will then be `\color{red}{16" balls"}`

What happens if you add another four red balls? You now have `36+4=40` balls total, and `8+4=12` red balls. What is the new ratio?

Your NEW ball count:
Green `12` balls
Red `12` balls
Blue `16` balls

Green - red - blue is 12-12-16. We see that the green to red ratio is `12:12` which is basically 1-to-1 (they are the same amounts, always).
And the green/red (since they are the same) to blue ratio would be
`12:16` which can be simplified to `6:8` then `3:4`

Your answer for the third question will be `\color{red}{1:1}`.