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 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 $s$ $tax = \begin{cases} 0 &0\leq s \leq 5000 \\ (0.25)(s-5000) &5000 < s \leq 10000 \\ 1250+(0.4)(s-10000) &10000 < s \leq 20000 \\ 5250+ (0.6)(s-20000) &20000 < s \end{cases}$ 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 $(0.25)(s-5000) = (0.33)(s)$ $-1250 = 0.8s$ which gives us a negative salary so $s > 10000$ If $10000 < s \leq 20000$ $1250 + (0.4)(s-10000) = 0.33s$ $1250 - 4000 = -0.07s$ $s=39285.7$ but this violates $s < 20000$ so $s > 20000$ $5250 + (0.6)(s-20000) = 0.33s$ $5250 - 12000 = -0.27s$ $s = 25000$ and this is your answer. Thanks from Student2018 April 12th, 2018, 04:36 AM   #3
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 Originally Posted by romsek Let the salary be $s$ $tax = \begin{cases} 0 &0\leq s \leq 5000 \\ (0.25)(s-5000) &5000 < s \leq 10000 \\ 1250+(0.4)(s-10000) &10000 < s \leq 20000 \\ 5250+ (0.6)(s-20000) &20000 < s \end{cases}$ 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 $(0.25)(s-5000) = (0.33)(s)$ $-1250 = 0.8s$ which gives us a negative salary so $s > 10000$ If $10000 < s \leq 20000$ $1250 + (0.4)(s-10000) = 0.33s$ $1250 - 4000 = -0.07s$ $s=39285.7$ but this violates $s < 20000$ so $s > 20000$ $5250 + (0.6)(s-20000) = 0.33s$ $5250 - 12000 = -0.27s$ $s = 25000$ and this is your answer.
Thanks a lot, but might there be a slightly simpler way to solve it, or is this the only method? April 12th, 2018, 11:07 AM   #4
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 Originally Posted by Student2018 Thanks a lot, but might there be a slightly simpler way to solve it, or is this the only method?
you can start with $s > 20000$ and that will get you the answer on the first try.

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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Poonarge Elementary Math 2 July 30th, 2015 07:16 AM bd_8_bc1601 Elementary Math 2 August 15th, 2012 06:53 PM Niko Bellic Algebra 1 November 12th, 2011 01:18 AM flux Elementary Math 2 May 1st, 2010 02:42 PM bentz69 Algebra 8 March 10th, 2010 05:47 AM

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