Three individuals form a partnership and agree to divide the profits equally. X invests $4,500, Y invests $4,500, Z invests $1,000. If the profits are $1,500 how much does X receive than if the profits were divided in proportion to the amount invested
X would receive $750 more than if the profits were divided in proportion to the amount invested.
To find out how much X receives in comparison to if the profits were divided in proportion to the amount invested, we need to calculate two scenarios:
1. Equal division of profits: In this scenario, since the profits are divided equally among the three partners, each partner receives an equal share. So, to calculate X's share, we divide the total profits ($1,500) by the number of partners (3):
X's share = Total profits / Number of partners = $1,500 / 3 = $500
2. Proportional division of profits: In this scenario, the profits are divided in proportion to the amount invested by each partner. To calculate X's share, we need to determine the total amount invested and then calculate X's proportional share:
Total amount invested = X's investment + Y's investment + Z's investment
= $4,500 + $4,500 + $1,000
= $10,000
X's proportional share = (X's investment / Total amount invested) x Total profits
= ($4,500 / $10,000) x $1,500
= (0.45) x $1,500
= $675
Therefore, if the profits were divided in proportion to the amount invested, X would receive $675.
To answer the question of how much more or less X receives compared to equal division, we subtract X's equal division share from X's proportional share:
Difference = X's proportional share - X's equal division share
= $675 - $500
= $175
Therefore, in this scenario, X would receive $175 more than if the profits were divided equally.
To calculate how much X receives compared to if the profits were divided in proportion to the amount invested, follow these steps:
Step 1: Calculate the total amount invested.
Total investment = X's investment + Y's investment + Z's investment
Total investment = $4,500 + $4,500 + $1,000
Total investment = $10,000
Step 2: Calculate the proportion of each individual's investment.
X's proportion = X's investment / Total investment
X's proportion = $4,500 / $10,000
X's proportion = 0.45
Y's proportion = Y's investment / Total investment
Y's proportion = $4,500 / $10,000
Y's proportion = 0.45
Z's proportion = Z's investment / Total investment
Z's proportion = $1,000 / $10,000
Z's proportion = 0.1
Step 3: Calculate the share of each individual's profit based on their proportion.
X's share = X's proportion * Total profit
X's share = 0.45 * $1,500
X's share = $675
Y's share = Y's proportion * Total profit
Y's share = 0.45 * $1,500
Y's share = $675
Z's share = Z's proportion * Total profit
Z's share = 0.1 * $1,500
Z's share = $150
Step 4: Calculate the difference in X's share based on equal distribution.
X's share with equal distribution = Total profit / Number of partners
X's share with equal distribution = $1,500 / 3
X's share with equal distribution = $500
Difference = X's share - X's share with equal distribution
Difference = $675 - $500
Difference = $175
Therefore, X receives $175 more than if the profits were divided in proportion to the amount invested.