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Number Problem: Number relationships

The smaller of two numbers is 9 less than the larger, and their sum is 37. Find the numbers.
 
Solution:
 
Based on the problem statement, the following representation is derived:
 
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Number Problem: Find two numbers

Problem: Find two numbers whose sum is 7 provided that one is 3 times the other.
 
Solution:
 
Based on the problem statement, the following representation is derived:
 
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Number Problem: Sum of two numbers

The sum of two numbers is 9 and their difference is 6. What are the numbers? Read more »

Business Venture Problem

Investment Problem
A woman invested in two business ventures. Last investment moneyyear she made a profit of 15 percent from the first venture but lost 5 percent from the second venture.

If last year's income from the two investments was equivalent to a return of 8 percent on the entire amount invested, how much had she invested in each venture?

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Stockholders' Profit Share

Profit Sharing
profit sharing problem
The profits of a business are shared among three stockholders. The first stockholder receives twice as much as the second and the second receives three times as much as the third. If the profits for last year were $26,400, how much did each stockholder receive?


Solution
This type of problem can be solved using equations in one variable only. This is possible since we can express one unknown value in terms of the other. Thus,

Let

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