Let me post the solution. Frankestein's solution seems great!
Here it is:
We are told that some of the stock at a shop is blue, some is red, and some must be other colors. We are asked to find how much of the stock that the store sold was red, in terms of m, the amount of blue stock sold.
The red stock was 1/6 of the store's total stock, which means that 5/6 of the stock was not red. We know that m is equal to one quarter of the stock that was not red, which means that m is 1/4 of 5/6 of the store's total stock, or 5/24 of the total stock.
The ratio of red stock to blue stock is constant, so we can use the fractions we already know to represent both the fraction of the stock that is red 1/6 and the fraction that is blue 5/24, and put them into a ratio equivalent to the ratio of red to blue generally: (1/6)/(5/24) = R/m.
Since dividing by a fraction is the same as multiplying by its reciprocal, we can simplify the left-hand side of the equation by multiplying by 24/5 to get 4/5.
Now we have (4/5)=R/m.
