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)

 

[Architeuthis Dux]

I understand that ratio is a comparison of two quantities and is often expressed in the form of a fraction or ratio notation. In this problem, the ratio of 24:9 represents the proportion of investment made by Mr Smith and Mr Jones respectively. This ratio was determined by dividing the total investment made by each partner by the total time (in months) that they were invested for.

In this case, Mr Smith invested $50,000 for 12 months, while Mr Jones invested $25,000 for 9 months. So the ratio is calculated as (50,000 x 12) : (25,000 x 9) = 600,000 : 225,000 = 24 : 9.

To determine how much each partner receives from the profit of $11,000, we use the ratio of 8:3, which is equivalent to the original ratio of 24:9. This means that for every 8 parts of the profit, Mr Smith receives 8/11 and Mr Jones receives 3/11.

Therefore, Mr Smith receives 8/11 x $11,000 = $8,000 and Mr Jones receives 3/11 x $11,000 = $3,000.

In conclusion, the ratio of 24:9 was determined by dividing the total investment made by each partner by the total time (in months) that they were invested for. This ratio was then used to determine the proportion of profit received by each partner.