Help with Ratio: Mr Smith & Mr Jones 24:9

[Gringo123]

Here is a problem involving ratio , and the answer plus work as given by my textbook. I get a little lost at the underlines part. I don't understabnd how we arrived at a ratio of 24:9. Can anyone help me out?

Mr Smith starts a business with $50,000.
3 months later, Mr Jones joins the business. He invests $25,000.
The profit at the end of the year is $11,000. It is divided in proportion to how much was invested and for how long.

How much does each partner receive?

ANSWER

Mr Smith invests $50,000 for 12 months.
Mr Jones invests $25,000 for 9 months.
Ratio = 50,000 x 12: 25,000 x 9
= 24:9
= 8:3
$11,000 is divided in ratio 8:3

Mr S has 8/11 x 11,000 = $8,000
Mr J has 3/11 x 11,000 = $3,000

 

[tiny-tim]

… I don't understabnd how we arrived at a ratio of 24:9. Can anyone help me out?
…
Mr Smith invests $50,000 for 12 months.
Mr Jones invests $25,000 for 9 months.
Ratio = 50,000 x 12: 25,000 x 9
= 24:9

Hi Gringo123!

If they invested the same amount, it would be 12:9, wouldn't it?

But Smithy invested twice as much, so it's 24:9.

(alternatively, you can treat the ":" as a "/" …

if you multiply it out, 50x12/25x9 = 24/9)