Three individuals form a partnership and agree to divide the profits equally. X invests $4,500, Y invests $4,500, and Z invests $1,000. If the profits are $1,500, how much less does X receive than if the profits were divided in proportion to the amount invested?
Equal divisions: x receives $500
Proportional: x receives
4500/(4500+4500+1000) * 1500 = $675
Well, let's see. If the profits were divided in proportion to the amount invested, we need to find out the ratio of each person's investment to the total investment.
Total investment = $4,500 + $4,500 + $1,000 = $10,000
X's share = (X's investment / Total investment) x Total profits
X's share = ($4,500 / $10,000) x $1,500 = $675
If the profits were divided equally, X would receive $500 less than his proportional share. So, X would receive $175 less than if the profits were divided in proportion to the amount invested.
To find out how much less X receives compared to if the profits were divided in proportion to the amount invested, we need to calculate the proportion of the investment made by each individual.
The total investment is given by:
Total investment = X's investment + Y's investment + Z's investment
Total investment = $4,500 + $4,500 + $1,000
Total investment = $10,000
The proportion of X's investment out of the total investment is given by:
X's proportion = X's investment / Total investment
X's proportion = $4,500 / $10,000
X's proportion = 0.45 or 45%
Similarly, we can calculate the proportion of Y's investment:
Y's proportion = Y's investment / Total investment
Y's proportion = $4,500 / $10,000
Y's proportion = 0.45 or 45%
Finally, we can calculate the proportion of Z's investment:
Z's proportion = Z's investment / Total investment
Z's proportion = $1,000 / $10,000
Z's proportion = 0.1 or 10%
Now, let's calculate the amount X would receive if the profits were divided in proportion to the amount invested:
X's share = X's proportion * Total profits
X's share = 0.45 * $1,500
X's share = $675
Since X's original investment is $4,500 and X receives $675, we can calculate the difference:
Difference = Original share - Proportional share
Difference = $4,500 - $675
Difference = $3,825
Therefore, X receives $3,825 less than if the profits were divided in proportion to the amount invested.
To solve this problem, we need to calculate how the profits would be divided if they were distributed proportionally to the amount each person invested.
First, let's calculate the total amount invested by all three individuals:
Total investment = X's investment + Y's investment + Z's investment
Total investment = $4,500 + $4,500 + $1,000
Total investment = $10,000
Next, we calculate the proportion of each individual's investment out of the total investment:
X's proportion = X's investment / Total investment
X's proportion = $4,500 / $10,000
X's proportion = 45%
Y's proportion = Y's investment / Total investment
Y's proportion = $4,500 / $10,000
Y's proportion = 45%
Z' s proportion = Z's investment / Total investment
Z's proportion = $1,000 / $10,000
Z's proportion = 10%
Now, we can calculate how much each person would receive if the profits were divided proportionally to their investment:
X's share = X's proportion * Total profit
X's share = 45% * $1,500
X's share = $675
Y's share = Y's proportion * Total profit
Y's share = 45% * $1,500
Y's share = $675
Z's share = Z's proportion * Total profit
Z's share = 10% * $1,500
Z's share = $150
Now, let's calculate how much less X receives compared to the proportional division:
Difference = X's equal share - X's proportional share
Difference = $1,500 / 3 - $675
Difference = $500 - $675
Difference = -$175
Based on these calculations, X receives $175 less compared to the proportional division of profits.