Question

Henri has $24,000 invested in stocks and bonds. The amount in stocks is $6,000 more than three times the amount in bonds. How much is each investment?

Answer 1

The amount of investment in bonds is US$ 4,500 and the amount of investment in stocks is US$ 19,500

Explanation:

Total investment in stocks and bonds = US$ 24,000

Amount of investment in bonds = x

Amount of investment in stocks = 3x + 6,000 (amount in stocks is $6,000 more than three times the amount in bonds)

For finding the value of x (amount of investment in bonds), we use this equation:

x + 3x + 6,000 = 24,000

x + 3x = 24,000 - 6,000

4x = 18,000

x = 4,500 (dividing by 4)

The amount of investment in bonds is US$ 4,500

Now let's find the amount of investment in stocks:

3x + 6,000 = 3 (4,500) + 6,000 = 13,500 + 6,000 = 19,500

The amount of investment in stocks is US$ 19,500

Answer 2

Investment in stocks= $19.500

Investment in bonds= $4.500

Explanation:

1. Because of the first sentence you know that the amount of money invested in both stocks and bonds is $24.000, then if "s" is the amount of money spend in stocks and "b" the amount of money spend in bonds,
   `b+s=24000`
2. Then, you are told that the amount of money invested in stocks is $6.000 more than three times the amount in bonds, which means that
   `s= 6.000+3*{b}`
3. We have two equations and two unknown variables (s and b): from the first equation we can say that
   `s=24.000-b`, while from the second equation we have that
   `s=6.000+3*{b}`.
4. Using these two equation we can say that
   `24.000-b=6.000+3*{b}`, from which we obtain
   `b=4.500`.
5. Then, using this last result, and replacing it into the first equation we get that
   `s=19.500`