# Math and Science Solutions for Businesses/math word problem

Question
An apartment building contains 12 units consisting of
one- and two-bedroom apartments that rent for \$360 and
\$450 per month, respectively. When all units are rented, the
total monthly rental is \$4,950. What is the number of twobedroom apartments?

Let x = number of 1-bedroom units and y = 2-bedroom units. Then, when all the units are rented

x + y = 12

and

x(360) + y(450) = 4950.

Substitute for x in terms of y  -> x = 12-y

(12-y)(360) + y(450) = 4950.

Solving for y,

12(360)-y(360) + y(450) = 4950  ->  y(450-360) = 4950-12(360) or  y(90) = 630

y = 630/90 = 7  and x = 5.

Plugging these back in gives the right answer.

Math and Science Solutions for Businesses

Volunteer

#### Randy Patton

##### Expertise

Questions regarding application of mathematical techniques and knowledge of physics and engineering principles to product and services design, optimization, prediction, feasibility and implementation. Examples include sales and product performance projections based on math/physics models in addition to standard regression; practical and cost effective sensor design and component configuration; optimal resource allocation using common tools (eg., MS Office); advanced data analysis techniques and implementation; simulation and "what if" analysis; and innovative applications of remote sensing.

##### Experience

26 years as professional physical scientist and project manager for elite research company providing academic quality basic and applied research for government and defense industry clients (currently retired). Projects I have been involved in include: - Notional sensor performance predictions for detecting underwater phenomena - Designing and testing guidance algorithms for multi-component system - Statistical analysis of ship tracking data and development of anomaly detector - Deployed vibration sensors in Arctic ice floes; analysis of data - Developed and tested ocean optical instrument to measure particles - Field testing of protoype sonar system - Analysis of synthetic aperture radar system data for ocean surface measurements - Redesigned dust shelters for greeters at Burning Man Festival Project management with responsibility for allocation and monitoriing of staff and equipment resources.

Publications
“A Numerical Model for Low-Frequency Equatorial Dynamics” (with Mark A. Cane), J. of Phys. Oceanogr., 14, No. 12, pp. 18531863, December 1984.

Education/Credentials
MIT, MS Physical Oceanography, 1981 UC Berkeley, BS Applied Math, 1976

Past/Present Clients
Am also an Expert in Advanced Math and Oceanography