Answer:
The purchase price of the house is $94,000
Explanation:
Let the amount invested by David be b, then the amount used to purchase the house would be 100,000 - b
If he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320
Then,
[tex]\frac{1}{3}b × 4% + \frac{2}{3}b × 6% = 320[/tex]
[tex]\frac{b}{3} × \frac{4}{100} + \frac{2b}{3} × \frac{6}{100} = 320[/tex]
[tex]\frac{4b}{300} + \frac{12b}{300} = 320[/tex]
[tex]\frac{16b}{300} = 320[/tex]
16b = 320 × 300
b = 320 × 300/16
b = 6,000
Therefore, the cost of the house (100,000 - b)
= 100,000 - 6,000
= $94,000
