### Instruction: Betty goes to the store to get flour and sugar.  The amount of flour she buys, in pounds, is at least 6 pounds more than half the amount of sugar, and is no more than twice the amount of sugar.  Find the least number of pounds of sugar that Betty could buy.### Response: To solve this problem, I need to translate the given information into inequalities and find the range of possible values for the amount of flour and sugar.
Let F be the amount of flour in pounds, and S be the amount of sugar in pounds. Then I have two inequalities: F >= 6 + S/2 and F <= 2S.
I want to find the least value of S that satisfies both inequalities, so I need to combine them in some way.
One way to do this is to use the second inequality to substitute for F in the first one. That is, since F <= 2S, I can write 2S >= 6 + S/2.
Now I have one inequality with one variable, which I can solve by isolating S.
To do that, I need to get rid of the fractions, so I multiply both sides by 2, which gives me 4S >= 12 + S.
Then I subtract S from both sides, which gives me 3S >= 12.
Then I divide both sides by 3, which gives me S >= 4.
This means that the smallest possible value of S is 4, and this is the least number of pounds of sugar that Betty could buy.