212k views
2 votes
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?

1 Answer

6 votes

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.

User Christian Baumann
by
8.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories