GMAT CLUB OLYMPICS: On a market, two merchants sold total of 100 pinea

Given: On a market, two merchants sold total of 100 pineapples and earned the same amount of money. If the first merchant had sold the second merchants pineapples at first merchant's price per pineapple, he would earned $15 and if the second merchant had sold the first merchants pineapples at second merchant's price per pineapple, he would earned \(\$6\frac{2}{3}\).

Asked: How many pineapples did the second merchant sell ?

Let the pineapples sold by second merchant be x.
Pineapples sold by first merchant = 100 - x

Let the first merchant's price per pineapple be p1 and second merchant's price per pineapple be p2.

On a market, two merchants sold total of 100 pineapples and earned the same amount of money.
p1 (100-x) = p2 x
p1 /p2 = x/(100-x) (1)

If the first merchant had sold the second merchants pineapples at first merchant's price per pineapple, he would earned $15.
x p1 = 15 (2)

if the second merchant had sold the first merchants pineapples at second merchant's price per pineapple, he would earned \(\$6\frac{2}{3}\)
(100-x)p2 = 6 2/3 = 20/3 (3)

(2)/(3)

xp1/(100-x)p2 = 15*3/20 = 9/4
{x/(100-x)}^2 = 9/4
x/(100 - x) = 3/2
2x = 300 - 3x
5x = 300
x = 300/5 = 60


IMO D