A man invested half of his money at 5%, one-third of his money at 4%, and the rest of his money at 5.5%. If his total investment income was $570, how much had he invested?
and please show me the solution to solve this problem. thanx
sorry bobpursly I cant understand your solution how can i compute this?
1/2 + 1/3 = 5/6, so
.05 * x/2 + .04 * x/3 + .055 * x/6 = 570
multiply by 6 to clear fractions:
.05 * x * 3 + .04 * x * 2 + .055 * x = 6*570
.15x + .08x + .055x = 3420
.285x = 3420
x = 12000
.05 * 6000 = 300
.04 * 4000 = 160
.055 * 2000 = 110
Total: 570
To solve this problem, we can break it down into steps:
Step 1: Set up equations for each investment:
Let's say the total amount of money the man had invested is "X" dollars.
The amount invested at 5%: 0.5X
The amount invested at 4%: (1/3)X
The amount invested at 5.5%: (1 - 0.5 - 1/3)X
Step 2: Calculate the income from each investment:
The income from the investment at 5%: 0.5X * 0.05 = 0.025X
The income from the investment at 4%: (1/3)X * 0.04 = 0.0133X
The income from the investment at 5.5%: (1 - 0.5 - 1/3)X * 0.055 = 0.0222X
Step 3: Set up the equation for the total investment income:
The total investment income is given as $570. We can add up the income from each investment and set it equal to 570:
0.025X + 0.0133X + 0.0222X = 570
Step 4: Solve for X:
Combine like terms on the left side of the equation:
0.0605X = 570
Divide both sides of the equation by 0.0605 to isolate X:
X = 570 / 0.0605
Use a calculator to obtain the value of X:
X ≈ 9412.396
Therefore, the man had invested approximately $9412.40.
Let me know if I can help you with anything else.