I'm having trouble how to set up this math problem:
Rebecca Herst received a year-end bonus of $17,000 from her company and invested the money in an account paying 6.5%. How much additional money should she deposit in an account paying 5% so that the return on the two investments will be 6%?
amount invested at 5% ----- x
solve for x
.05x + .065(17000) = .06(17000 + x)
times 200
10x + 13(17000) = 12(17000 + x)
take it from there.
Thanks
To set up this math problem, we need to determine the amount of additional money that Rebecca should deposit in an account paying 5% so that the overall return on her investments will be 6%.
Let's break down the problem into smaller parts.
Step 1: Calculate the return on the $17,000 invested at 6.5%.
To find the return on an investment, you multiply the principal amount by the interest rate as a decimal. In this case, the principal amount is $17,000 and the interest rate is 6.5% (0.065 as a decimal).
Return on the investment = $17,000 × 0.065
Step 2: Calculate the return required on the total investment at 6%.
Since the overall return should be 6% and Rebecca has already invested $17,000 at 6.5%, we need to determine the return required on the additional amount invested at 5%.
Return required on the total investment = (Total investment) × 0.06
Step 3: Determine the additional amount Rebecca needs to deposit in the account paying 5%.
Let's assume she needs to deposit an additional amount of x dollars at 5%.
Return on the additional investment = x × 0.05
Step 4: Determine the equation by equating the two returns.
Since the return required on the total investment should be equal to the return on the $17,000 invested at 6.5% plus the return on the additional investment at 5%, we can set up the equation:
Return on the investment at 6% = Return on the $17,000 invested at 6.5% + Return on the additional investment at 5%
0.06(17000 + x) = (17000 × 0.065) + (x × 0.05)
Step 5: Solve the equation to find the value of x.
Simplifying the equation, we have:
0.06(17000 + x) = (17000 × 0.065) + (x × 0.05)
1020 + 0.06x = 1105 + 0.05x
Now, subtract 0.05x from both sides of the equation:
0.06x - 0.05x = 1105 - 1020
0.01x = 85
Lastly, divide both sides of the equation by 0.01:
x = 85 / 0.01
x = 8500
Therefore, Rebecca should deposit an additional $8,500 in an account paying 5% so that the return on her investments will be 6%.