­A certain café sells bagels for $1.10 and muffins for $1.50

devashish2407
Given: A certain café sells bagels for $1.10 and muffins for $1.50. Last Wednesday, muffins accounted for M percent of all revenue from baked goods, and b percent of the baked goods sold were bagels.
Asked: If the café sold only muffins and bagels last Wednesday, which of the following expresses the value of M in terms of b ?
Let the number of bagels sold be x & number of muffins sold be y.

Revenue from baked goods = 1.1x + 1.5y
Revenue from muffins = 1.5y

M% = 1.5y/(1.1x + 1.5y) * 100%
(1.1x + 1.5y)*M = 150y
1.1Mx + 1.5My = 150y
1.1Mx = (150-1.5M)y
\(\frac{x}{y} = \frac{(150-1.5M)}{1.1M} = \frac{15}{11} * \frac{(100-M)}{M}\)

Baked goods sold = x+ y
b% = x/(x+y) *100%
(x + y)b = 100x
(100 - b)x = by 
\(\frac{x}{y} =\frac{ b}{(100-b)} = \frac{(150-1.5M)}{1.1M} = \frac{1.5}{1.1} *\frac{(100-M)}{M}= \frac{15}{11} * \frac{(100-M)}{M} \)
\(\frac{(100-M)}{M} = \frac{11b}{15(100-b)}\)
\(\frac{M}{100} = \frac{15(100-b)}{(1500-4b)}\)
\(M = \frac{1500(100-b)}{(1500-4b)} = \frac{375(100-b)}{(375-b)}\)

IMO E­