You are here:

# Advanced Math/Amount- Investments

Advertisement

Question
An amount is invested in bonds at 3 percent, real estate at 4 percent, and stocks at 5 percent.  The amount at 5 percent is half as much as the other two.

Income per year - \$490

Total invested- \$12,000

Calculate amount invested in each.

Answer
"An amount is invested in bonds at 3 percent, real estate at 4 percent, and stocks at 5 percent."
b, r, and s are the dollar amounts invested in bonds, real estate, and stocks, respectively.

"The amount at 5 percent is half as much as the other two."
This is ambiguous*. I think they mean "the amount at 5 percent is half THE SUM OF the other two."
s = (b+r)/2

"Total invested- \$12,000"
b + r + s = 12,000
b + r + (b+r)/2 = 12,000
2b + 2r + (b+r) = 24,000
3b + 3r = 24,000
b+r = 8,000
r = 8,000-b
s = (b+r)/2 = (b+(8000-b))/2 = 4,000

"Income per year - \$490"
0.03b + 0.04r + 0.05s = 490

substitution
0.03b + 0.04(8000-b) + 0.05(4,000) = 490
0.03b + 320 - 0.04b + 200 = 490
b = 3,000
r = 8,000-b = 5,000

\$3,000 is invested in bonds at 3%
\$5,000 is invested in real estate at 4%
\$4,000 is invested in stocks at 5%
=====
*I first interpreted this as "the amount at 5 percent is half as much as the amount invested in either of the other two."
This would mean that s = b/2 = r/2, which in turn gives b=r=4,800 and s=2,400. This gives the wrong amount of interest income:
0.03·4,800 + 0.04·4,800 + 0.05·2,400 = \$456
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Prompt, friendly, thorough reply !

• Add to this Answer
• Ask a Question

Advanced Math

All Answers

Ask Experts

Volunteer

#### Janet Yang

##### Expertise

I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

##### Experience

I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

Publications
Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language

Education/Credentials
I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley.

Past/Present Clients
George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

©2016 About.com. All rights reserved.

Browse Answers: