Answer
Dr. Willians will need to invest $20,000 at 8% so that his total interest on the two investments will be 7% of the two investments.
Step-by-step explanation
If any amount, P, is invested at a rate of R%, the interest on top will be calculated as
Interest = (PR/100)
Let the amount of money invested at 8% be x dollars
The amount of interest generated on $10,000 at a rate of 5% will be
Interest = (5 × 10,000)/100 = 500 dollars
Amount of interest generated on x dollars at 8% is
Interest = (8 × x)/100 = 0.08x
Total interest on the two investments = (500 + 0.08x) dollars
We are then told that this total interest has to be 7% of the two investments (10,000 + x) dollars
This total interest can then be calculated as
Total Interest = 7% × (10,000 + x)
= 0.07 (10,000 + x)
= (700 + 0.07x) dollars
Equating these to each other
(500 + 0.08x) = (700 + 0.07x)
500 + 0.08x = 700 + 0.07x
0.08x - 0.07x = 700 - 500
0.01x = 200
Divide both sides by 0.01
(0.01x/0.01) = (200/0.01)
x = 20,000 dollars
Hope this Helps!!!