Problems Involving Ratios

Example:
The monthly salaries of Richard and Tom were in the ratio of 5 : 6. When Richard’s salary increase by $200 and Tom’s salary increase by $330, the ratio of their salaries became 4 : 5. Find their original monthly salaries.

Solution:
So let’s Richard’s salary is 5n and Tom’s salary is 6n, where n is constant.
To find new salary of Richard’s = $(5n+200)
To find new salary of Tom’s = $(6n+330)
5n+200 over 6n+330 = 4 over 5
Then, we do something called “Cross Multiply.”
5(5n+200) = 4(6n+330)
And it becomes, 25n+1,000 = 24n+1,320
n = 320
Richard’s monthly salary = 5 x 320 = $1,600
Tom’s monthly salary = 6 x 320 = $1,920

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