Three individuals form a partnership and agree to divide the profits equally. X invests $4,500, Y invests $3,500 and Z invests $2,000. If the profits are $1,500, how much less does X receive than if the profits were divided in proportion to the amount invested?
Divided proportionally,
9x+7x+4x=1500
x=75
so X:Y:Z = 675:525:300
So, 675-500 = 175 less
how did u get 9x+7x+4x=1500
The amount that X invested is 45% of total investment
So the profit X receives must be 45%*1500=676
But X received the same amount as other 2 investors: 1500:3=500
So X received (675-500)=175 less than he should receive
Sorry for the mistake in my previous response. Here's the correct solution:
The total amount invested is $4,500 + $3,500 + $2,000 = $10,000.
If the profits were divided proportionally to the amount invested, X would receive:
($1,500) x ($4,500/$10,000) = $675
Similarly, Y would receive:
($1,500) x ($3,500/$10,000) = $525
And Z would receive:
($1,500) x ($2,000/$10,000) = $300
Therefore, X would receive $500 in the equal profit sharing arrangement, so X would receive $175 less than if the profits were divided proportionally to the amount invested.
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 the total investment made by each partner.
The total investment is the sum of the individual investments: $4,500 + $3,500 + $2,000 = $10,000.
Now, let's calculate the proportion for each partner:
X's proportion = X's investment / Total investment = $4,500 / $10,000 = 0.45
Y's proportion = Y's investment / Total investment = $3,500 / $10,000 = 0.35
Z's proportion = Z's investment / Total investment = $2,000 / $10,000 = 0.20
Next, we need to calculate the share of profits each partner would receive if the profits were divided in proportion to their investment.
X's share of profits = X's proportion * Total profits = 0.45 * $1,500 = $675
Y's share of profits = Y's proportion * Total profits = 0.35 * $1,500 = $525
Z's share of profits = Z's proportion * Total profits = 0.20 * $1,500 = $300
Now, let's find out the difference in X's share if the profits were divided equally and if they were divided according to the proportion of investment:
If the profits were divided equally among the three partners, X would receive $1,500 / 3 = $500.
Therefore, the difference in X's share is $675 - $500 = $175 less than if the profits were divided in proportion to the investment.
So, X receives $175 less than if the profits were divided in proportion to the amount invested.