1. Alcoa stock traded at $70 per share. Pete and his partner Al decided to sell 100 shares for a total of $7,000. The stock was purchased for $65 per share (100 x $65 = $6,500) for a gain of $500. Pete invested twice as much as Al in the purchasing of the shares. How much should Pete receive and how much should Al receive of the gain? Round to the nearest cent
500/3 = 166.67 >> Al's share
To find out how much Pete and Al should receive of the gain, let's first determine their original investments.
If Pete invested twice as much as Al, then let's say Al invested x dollars.
So, Pete's investment would be 2x dollars.
The total investment of both Pete and Al is given as $6,500.
Thus, we have the equation: x + 2x = $6,500.
Combining like terms, we get: 3x = $6,500.
Dividing both sides of the equation by 3, we find: x = $2,166.67 (rounded to the nearest cent).
Therefore, Pete invested $2,166.67 and Al invested $4,333.33.
Next, let's calculate the gain of $500.
To find out the proportion of the gain each should receive, we need to determine the total investment:
Total Investment = Pete's Investment + Al's Investment
Total Investment = $2,166.67 + $4,333.33 = $6,500.
Finally, we can calculate the proportion of the gain for each person:
Pete's Share = (Pete's Investment / Total Investment) * Gain
Al's Share = (Al's Investment / Total Investment) * Gain
Pete's Share = ($2,166.67 / $6,500) * $500 ≈ $166.95 (rounded to the nearest cent)
Al's Share = ($4,333.33 / $6,500) * $500 ≈ $333.05 (rounded to the nearest cent)
Therefore, Pete should receive approximately $166.95 of the gain, and Al should receive approximately $333.05 of the gain.
To determine how much Pete and Al should receive from the gain, we need to calculate their respective investments in the shares and then divide the gain proportionally.
Let's start by finding out Pete's and Al's investments.
We know that Pete invested twice as much as Al in the purchasing of the shares. Let's represent Al's investment as "x." Therefore, Pete's investment would be 2x.
Next, let's calculate the cost of Pete's and Al's investments:
Cost of Al's investment = Number of shares (100) × Cost per share ($65) = $6,500
Since Pete's investment is twice that of Al, we can calculate it as:
Cost of Pete's investment = 2 × Cost of Al's investment = 2 × $6,500 = $13,000
Now, let's calculate the gain:
Gain = Total amount received ($7,000) − Cost of investment ($6,500) = $500
To determine the proportion of the gain that each of them should receive, we need to calculate their shares based on their investments.
Proportion of gain for Al = Al's investment / (Pete's investment + Al's investment)
Proportion of gain for Pete = Pete's investment / (Pete's investment + Al's investment)
Proportion of gain for Al = $6,500 / ($13,000 + $6,500) = $6,500 / $19,500 ≈ 0.3333
Proportion of gain for Pete = $13,000 / ($13,000 + $6,500) = $13,000 / $19,500 ≈ 0.6667
Now, let's calculate the amount of the gain that each of them should receive:
Amount of gain for Al = Proportion of gain for Al × Total gain
Amount of gain for Pete = Proportion of gain for Pete × Total gain
Amount of gain for Al = 0.3333 × $500 ≈ $166.65
Amount of gain for Pete = 0.6667 × $500 ≈ $333.35
Therefore, Pete should receive approximately $333.35 of the gain, and Al should receive approximately $166.65.