Question

Calvin purchased some candles at 3 for $ 5 and sold them at 5 for $ 12. Thus, Calvin gained $ 143 in all. How many candles did Calvin purchase?

Answer 1

3candles = 5$ (purchase price)
1 candle = 5/3

5 candles = 12$ (selling price)
1 candle = 12/5

Let no. of candles bought be X
price of candles sold - price of candles purchased = 143$

$price \: of \: candles \: sold = \frac{12x}{5} \\ price \: of \: candles \: purchased \: = \frac{5x}{3} \\ \frac{12x}{5} - \frac{5x}{3} = 143 \\ 36x - 25x = 15 \times 143 \: \: (by \: taking \: lcm) \\ 11x = 2145 \\ x = \frac{2145}{11} \\ x = 195$
Hence, Calvin purchased 195 candles.
hope it helped.