To find out how much less X receives than if the profits were divided in proportion to the amount invested, we first need to determine the proportion of each person's investment to the total investment.
The total investment is the sum of X's, Y's, and Z's investments:
Total investment = $4,500 + $3,500 + $2,000 = $10,000
Now, let's find the proportion of X's investment to the total investment:
Proportion of X's investment = X's investment / Total investment = $4,500 / $10,000
Similarly, we can find the proportions for Y and Z:
Proportion of Y's investment = $3,500 / $10,000
Proportion of Z's investment = $2,000 / $10,000
To determine how much each person receives when the profits are divided in proportion to their investment, we multiply their respective proportions by the total profit of $1,500:
Amount X receives = Proportion of X's investment * Total profit = (0.45) * $1,500
Amount Y receives = Proportion of Y's investment * Total profit = (0.35) * $1,500
Amount Z receives = Proportion of Z's investment * Total profit = (0.2) * $1,500
We can now calculate these amounts:
Amount X receives = $675
Amount Y receives = $525
Amount Z receives = $300
To find out how much less X receives than if the profits were divided in proportion to the amount invested, we subtract the amount X actually receives from the amount X would receive in proportion to the amount invested:
Difference = Amount X receives in proportion to the amount invested - Amount X actually receives
Difference = ($4,500 / $10,000) * $1,500 - $675
Calculating this expression, we find:
Difference = $675
Therefore, X receives $675 less than if the profits were divided in proportion to the amount invested.