Lisa Chen invested $24,000, part at 8% and the rest at 7.2%. How much did she invest at each rate if her income from the 8% investment is two thirds that of the 7.2% investment?
part invested at 8% ---- x
part invested at 7.2% -- 24000-x)
income from first = .08x
income from 2nd = .072(24000-x)
.08x = (2/3)(.072)(24000-x)
.24x = .144(24000-x)
.24x = 3456 - .144x
.384x=3456
x = 9000
so $9000 invested at 8%
and $15000 invested at 7.2%
Let's assume Lisa Chen invested x dollars at 8% and (24000 - x) dollars at 7.2%.
According to the problem, her income from the 8% investment is two-thirds of the income from the 7.2% investment.
The income from the 8% investment can be calculated using the formula:
Income(8%) = Principal(8%) * Rate(8%)
Similarly, the income from the 7.2% investment can be calculated using the formula:
Income(7.2%) = Principal(7.2%) * Rate(7.2%)
From the problem, we have the equation:
Income(8%) = (2/3) * Income(7.2%)
Substituting the formulas for income, we get:
Principal(8%) * Rate(8%) = (2/3) * (Principal(7.2%) * Rate(7.2%))
Now, let's plug in the given values:
x * 0.08 = (2/3) * ((24000 - x) * 0.072)
Simplifying the equation:
0.08x = (2/3)(0.072)(24000 - x)
0.08x = (2/3)(1728 - 0.072x)
0.08x = 1152 - 0.048x
0.08x + 0.048x = 1152
0.128x = 1152
x = 1152 / 0.128
x = 9000
Therefore, Lisa Chen invested $9000 at 8% and $15000 (24000 - 9000) at 7.2%.
To solve this problem, we can set up two equations based on the given information. Let's solve it step by step:
Let's assume Lisa invested x dollars at 8% and (24000 - x) dollars at 7.2%.
First, we need to set up an equation for the income from the 8% investment being two-thirds that of the 7.2% investment.
The income from the 8% investment can be calculated as (8/100) * x = 0.08x.
The income from the 7.2% investment can be calculated as (7.2/100) * (24000 - x) = 0.072(24000 - x).
According to the given information, the income from the 8% investment is two-thirds that of the 7.2% investment. So, we can set up the equation:
0.08x = (2/3) * 0.072(24000 - x)
Now, let's solve the equation to find the value of x:
0.08x = (2/3) * 0.072(24000 - x)
0.08x = 0.048(24000 - x)
Multiply both sides of the equation by 100 to clear the decimals:
8x = 48(24000 - x)
8x = 1152000 - 48x
Combine like terms:
8x + 48x = 1152000
56x = 1152000
Divide both sides by 56 to isolate x:
x = 1152000 / 56
x ≈ 20571.43
So, Lisa invested approximately $20,571.43 at 8% and the remaining amount, which is (24000 - x), at 7.2%.
24000 - x ≈ 24000 - 20571.43
≈ 3428.57
Therefore, Lisa invested approximately $20,571.43 at 8% and $3,428.57 at 7.2%.