System Of Elimination:
Greg invested $11,000 in two accounts.
The first account pays 5% interest per year.
The second account pays 8% interest per year.
Greg earned a total of $752.50 in interest at the end of the first year.
How much did Greg invest in the 5% account?
~I don't know how to do these with interest
No worries! I can help you understand how to solve this problem using a system of elimination. Let's break it down step by step:
Step 1: Set up the equation
We need to find out how much Greg invested in the 5% account. Let's call the amount he invested in the 5% account "x". Since the total amount Greg invested is $11,000, we can express the amount he invested in the second account as "11,000 - x".
Step 2: Calculate the interest for each account
The interest earned from the first account can be calculated by multiplying the amount invested (x) by the interest rate of 5% (or 0.05). So, the interest earned from the first account is 0.05x.
Similarly, the interest earned from the second account is calculated by multiplying the amount invested in the second account (11,000 - x) by the interest rate of 8% (or 0.08). So, the interest earned from the second account is 0.08(11,000 - x).
Step 3: Set up the equation for the total interest earned
The problem states that Greg earned a total of $752.50 in interest at the end of the first year. Therefore, we can set up the equation:
0.05x + 0.08(11,000 - x) = 752.50
Step 4: Solve the equation
Now, we can solve the equation to find the value of "x", which represents the amount Greg invested in the 5% account. Here's how:
0.05x + 0.08(11,000 - x) = 752.50
0.05x + 880 - 0.08x = 752.50
0.05x - 0.08x = 752.50 - 880
-0.03x = -127.50
x = (-127.50) / (-0.03)
x = 4250
So, Greg invested $4250 in the 5% account.
I hope this explanation helps you solve similar problems with interest rates in the future. Let me know if there's anything else I can assist you with!
f + s = 11000
... 8 f + 8 s = 88000
5 f + 8 s = 75250
subtract equations to eliminate s
3 s = 12750