Question 1208330
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Hi
If Bob sells a TV at a discount of 15% of the marked price he will make a profit of $135. If he sells
at a discount of 25% of marked price he makes a loss of $65. What is the cost price of the TV. 

Let marked price be P, and cost price, C

A discount of 15% off of the marked price means that it'd be sold for 100% - 15% = 85% of the marked price, or .85P
Since a discount of 15% off of the marked price yields a PROFIT of $135, we get: .85P = C + 135 ----- eq (i)

A discount of 25% off of the marked price means that it'd be sold for 100% - 25% = 75% of the marked price, or .75P
Since a discount of 25% off of the marked price yields a LOSS of $65, we get: .75P = C - 65 ------ eq (ii)

               .85P = C + 135 ----- eq (i)
               .75P = C - 65 ------ eq (ii)
                .1P = 200 ----- Subtracting eq (ii) from eq (i) 
Marked price, or {{{matrix(1,7, P, "=", 200/.1, "=", "2,000"/1, "=", "$2,000")}}}

         .75(2,000) = C - 65 ----- Substituting 2,000 for P in eq (ii)
              1,500 = C - 65
         1,500 + 65 = C 
            <font color = red><font size = 4><b>$1,565</font></font></b> = C <font color = red><font size = 4><b>(Cost)</font></font></b></pre>