Math and Science Solutions for Businesses/COMPUTING PERCENTAGES

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Question
QUESTION: I WOULD LIKE TO KNOW HOW TO GO ABOUT COMPUTING THE PERCENTAGES, IF FOR EXAMPLE JOHN MADE A $250 IN CONTRIBUTION TO A BUILDING PROJECT THAT COST $3000, MEANING HIS PERCENTAGE CONTRIBUTION IS 8.333%, IF HE ALSO MAKES A $300 CONTRIBUTION TO PURCHASE FURNITURE WHICH COST $2250 TO BEAUTIFY THE BUILDING, MEANING HIS PERCENTAGE CONTRIBUTION IS 13.333%. HOW DO YOU FIND HIS TOTAL PERCENTAGE OF THE TWO PROJECTS(BUILDING AND FURNITURE)WHICH COST $5250 IN TOTAL.

ANSWER: John contributed $250 towards the $3000 costs to start. This happens to be 250/300 or 8.33%. He then contributed $300 towards the subsequent $2250 cost, or 300/2250 = 13.33%. The total contribution by John is $550 towards a total cost of $5250, so just like you calculated the percentages for the 2 pieces of the projects, John's total contribution to the total project is $550/$5250 = 10.48%.

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QUESTION: Can you then say that just like you added his contribution to get $550 then you can add the two percentages (8.33% and 13.33)and because it is for 200% (two different contributions) then finding the 100% of the sum of the two percentile would be 10.83 which when computer against the total amount ($5250)you get $568.575 which is 18.575 more that the actual. this is my challenge, is it possible to go the way i went?

Answer
The 2 cases have different amounts of money contributing to the total: $3000 + $2250 = $5250. You have to weight the percentages according the the fraction of the total that they correspond to:

(3000/5250)(8.33%) + (2250/5250)(13.33%) = 10.48%.

Your method is weights the 2 contributions equally which is why you get a different (erroneous) answer.

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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

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