Profit and loss 31 - 10th grade

From Homeworkwiki

Mr. Robinson altogether got $719.50 by selling a fridge at profit of 20% and a TV
at a profit of 15%. Had he sold the fridge at a profit of 25% and the TV at a profit
of 20% he would have got $30.50 more. Find the cost price of the fridge and TV.

Solution: Let $x and $y be respectively the cost price of the fridge and the TV.

So, from the 1st condition we have, (120/100)x + (115/100)y = 719 ½

Or, (6/5)x + (23/20)y = 1439/2…………..(i)

So, from the 2nd condition we have, (5/100)x + (5/100)y = 61/2

Or, x + y = 610…………..(ii)

Now from (i) we have 24x + 23y = 14390…………(iii)

Now solving (ii) and (iii) we have,

24x + 24y = 610 * 24 = 14640 and

24x + 23y = 14390

__________________________

(Subtracting) y = 250

So, x = 610 – 250 = 360

Hence, the cost price of the fridge = $360 and that of the TV = $250