Heather has divided $8000 between two investments, one paying 8% and the other paying 6%. If the return on her investment is $550 how much does she have in the larger investment?
Heather has divided $8000 between two investments , one paying 8% and the other paying 6%. If the return on her investment is $550 how much does she have in the larger investment?
Anderson Community College has formed a 26 person planning committee.There are 5 times as many administrators as there are students and 5 more faculty members than students.How many students are there on the committee?
Well, Heather seems to have quite the financial balancing act going on! Let's use a little humor to find out how much she has in the larger investment.
Now, since she has divided her money between two investments at different interest rates, it's like she's dealing with the "Carnival of Investments"! 🎪
Let's say she put x dollars in the larger investment, which pays 8% interest. That means she put (8000 - x) dollars in the other investment, which pays 6% interest.
Now, we know that the total return on her investments is $550, so the interest she earns from both investments can be written as:
0.08x (from the larger investment) + 0.06(8000 - x) (from the smaller investment)
Since she earns $550 in total, we can set up an equation:
0.08x + 0.06(8000 - x) = 550
Now, let's solve this equation and see how much she has in the larger investment:
0.08x + 0.06(8000 - x) = 550
0.08x + 480 - 0.06x = 550
0.02x + 480 = 550
0.02x = 550 - 480
0.02x = 70
x = 70 / 0.02
x ≈ 3500
So it looks like Heather has approximately $3500 in the larger investment! 🎉
Keep in mind, though, that investing can have its ups and downs, just like a clown balancing on a unicycle. It's always a good idea to monitor your investments and adjust accordingly.
To find out how much Heather has in the larger investment, let's proceed step by step.
Step 1: Set up the problem
We are given two investments: one paying 8% and the other paying 6%. The total amount invested is $8000, and the combined return on the investments is $550. We need to figure out the amount invested in the larger investment.
Step 2: Set up equations
Let x represent the amount invested in the larger investment. Then, the amount invested in the smaller investment would be $8000 - x.
Step 3: Calculate the return on each investment
The return on the larger investment can be calculated as 8% of x, which is 0.08x.
The return on the smaller investment can be calculated as 6% of ($8000 - x), which is 0.06($8000 - x).
Step 4: Formulate the equation
The total return on both investments is $550. Therefore, we can write the equation as:
0.08x + 0.06($8000 - x) = $550
Step 5: Solve the equation
Now, we can solve the equation to find the value of x, which represents the amount invested in the larger investment.
0.08x + 0.06($8000 - x) = $550
0.08x + $480 - 0.06x = $550
0.02x + $480 = $550
0.02x = $550 - $480
0.02x = $70
x = $70 / 0.02
x = $3500
Therefore, Heather has $3500 invested in the larger investment.
$x invested at 8%, then 8000-x invested at 6%
.08x + .06(8000-x) = 550
8x + 6(8000-x) = 55000
8x + 48000 - 6x = 55000
2x = 7000
x = 3500
so $3500 invested at 8%, and $4500 invested at 6%
check:
..08(3500) + .06(4500) = 550