
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 12th, 2018, 01:16 AM  #1 
Member Joined: Apr 2018 From: On Earth Posts: 34 Thanks: 0  Salary and percentages question
Tax is collected annually in the following manner: On the first £5000 earned, no tax is paid On the next £5000 earned, 25% tax is paid On the next £10000 earned, 40% tax is paid On any further income, 60% tax is paid. A sailor pays 33% of his salary in tax. What is his salary? Can anyone solve this? 
April 12th, 2018, 02:49 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,648 Thanks: 1476 
Let the salary be $s$ $tax = \begin{cases} 0 &0\leq s \leq 5000 \\ (0.25)(s5000) &5000 < s \leq 10000 \\ 1250+(0.4)(s10000) &10000 < s \leq 20000 \\ 5250+ (0.6)(s20000) &20000 < s \end{cases}$ let's try each case. We see 0 is a solution, but probably not the one they are looking for. if $5000< s \leq 10000$ then $(0.25)(s5000) = (0.33)(s)$ $1250 = 0.8s$ which gives us a negative salary so $s > 10000$ If $10000 < s \leq 20000$ $1250 + (0.4)(s10000) = 0.33s$ $1250  4000 = 0.07s$ $s=39285.7$ but this violates $s < 20000$ so $s > 20000$ $5250 + (0.6)(s20000) = 0.33s$ $5250  12000 = 0.27s$ $s = 25000$ and this is your answer. 
April 12th, 2018, 04:36 AM  #3  
Member Joined: Apr 2018 From: On Earth Posts: 34 Thanks: 0  Quote:
 
April 12th, 2018, 11:07 AM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 2,648 Thanks: 1476  Quote:
I purposefully showed you that the other ranges for $s$ didn't work. In general though you have to try each range until you find the right one.  

Tags 
percentages, question, salary 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Math Question  percentages  Poonarge  Elementary Math  2  July 30th, 2015 07:16 AM 
Salary calculation question  bd_8_bc1601  Elementary Math  2  August 15th, 2012 06:53 PM 
Question about Average Salary  Niko Bellic  Algebra  1  November 12th, 2011 01:18 AM 
Simple percentages question  flux  Elementary Math  2  May 1st, 2010 02:42 PM 
percentages question  bentz69  Algebra  8  March 10th, 2010 05:47 AM 