posted by jessica .
A baker needs between 40 pounds and 50 pounds of a flour-sugar mixture that contains ten times as much flour as sugar. What are the possible weights of flour the baker can use?
The question as it is does not restrict the answer to integral weights in pounds, so any between 40 and 50 pounds is a possible weight, W.
In order to satisfy the given proportion constraints, W/11=sugar, 10W/11=flour will ensure that the proportion be correct.
If the question specifies that the ingredient weights be integral (i.e. whole numbers), then W will have to be a multiple of 11, which makes 44 the only possible weight of mixture between 40 and 50, and the weight of flour is 10W/11=40 pounds.