please explain:
sam invested part of his $25,000 bonus in a fund that paid 8% profit and invested the rest in stock that suffered a 3% loss. Find the amount in each investment if his overall net profit was $1230.
Let Sam invested for profit = $ x
Thus other investment = $(25000 -x)
The profit = 8% of x= 0.08x
Loss = 3% of (25000-x) = 0.03(25000-x)
Thus 0.08x -0.03(25000-x) = 1230
We get x= 18,000
To solve this problem, let's break it down into smaller steps:
Step 1: Assign variables to the unknowns in the problem.
Let's assume that Sam invested a certain amount, denoted as "x," in the fund that paid 8% profit. The remaining amount, which he invested in the stock that suffered a 3% loss, will be "25,000 - x" (since his total bonus was $25,000).
Step 2: Calculate the profit from each investment.
The profit from the fund investment is calculated as x * 8% = 0.08x (since 8% can be written as 0.08).
The loss from the stock investment is calculated as (25,000 - x) * -3% = -0.03(25,000 - x) [since it suffered a 3% loss, which is equivalent to a negative 3% profit].
Step 3: Set up an equation based on the given information.
Since Sam's overall net profit was $1,230, we can set up the equation as follows:
Profit from fund investment + Loss from stock investment = Overall net profit
0.08x + (-0.03)(25,000 - x) = 1,230
Step 4: Solve the equation and find the value of x.
Let's solve the equation:
0.08x - 0.03(25,000 - x) = 1,230
0.08x - 0.03(25,000) + 0.03x = 1,230
0.08x - 750 + 0.03x = 1,230
0.11x - 750 = 1,230
0.11x = 1,230 + 750
0.11x = 1,980
x = 1,980 / 0.11
x ≈ 18,000
Step 5: Calculate the value of the remaining investment.
Since Sam invested $18,000 in the fund, the remaining amount invested in the stock will be:
25,000 - 18,000 = $7,000.
So, Sam invested $18,000 in the fund that paid 8% profit and $7,000 in the stock that suffered a 3% loss.