Question

3. You invested $11,000 in stocks and bonds paying 5% and 8% annual interest. If the total interest for the year was $730, how much was invested in each account?

4. A California company needs to blend a wine that is 6% alcohol, with a French wine which has a 9% content to obtain 200 gallons with a 7% alcohol content. How much of each kind should he use?

Answer 1

9514 1404 393

Answer:

3. $6000 at 8%; $5000 at 5%

4. 66 2/3 gallons of 9%; 133 1/3 gallons of 6%

Explanation:

For many mixture problems, it works well to let a variable represent the amount of the largest contributor used in the mix.

3. Let x represent the amount invested at 8%. Then the total interest is ...

8%x +5%(11000-x) = 730

3%x = 730 -550

x = 180/0.03 = 6000

$6000 was invested at 8%; $5000 was invested at 5%.

__

4. Let x represent the number of gallons of 9% content. Then the alcohol content of the mix is ...

9%x +6%(200 -x) = 7%(200)

3%x = 1%(200) . . . . . subtract 6%(200)

x = 200/3 = 66 2/3 . . . . . divide by 3%

200 -x = 133 1/3

66 2/3 gallons of 9% wine and 133 1/3 gallons of 6% wine should be used.