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.

Logic
Aug 28, 2018

#1**+2 **

**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.**

Let \(y\) = flour

Let \(x\) = sugar

\(\begin{array}{|rcll|} \hline y &\ge& 6+\dfrac x2 \\ y &\le& 2x \\ \hline \end{array}\)

\(\begin{array}{|rcll|} \hline && & y \ge 6+\dfrac x2 \\ && & y \le 2x \\\\ \underline{x_{\text{min}}:} \\ 2x &=& 6+\dfrac x2 \\\\ 2x-\dfrac x2 &=& 6 \\\\ \dfrac32\cdot x &=& 6 \\\\ x &=& \dfrac23 \cdot 6 \\\\ \mathbf{ x} & \mathbf{=} & \mathbf{4\ \text{pounds}} \\ \hline \end{array}\)

The least number of pounds of sugar that Betty could buy are \(\mathbf{4\ \text{pounds}}\).

heureka
Aug 29, 2018

#1**+2 **

Best Answer

**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.**

Let \(y\) = flour

Let \(x\) = sugar

\(\begin{array}{|rcll|} \hline y &\ge& 6+\dfrac x2 \\ y &\le& 2x \\ \hline \end{array}\)

\(\begin{array}{|rcll|} \hline && & y \ge 6+\dfrac x2 \\ && & y \le 2x \\\\ \underline{x_{\text{min}}:} \\ 2x &=& 6+\dfrac x2 \\\\ 2x-\dfrac x2 &=& 6 \\\\ \dfrac32\cdot x &=& 6 \\\\ x &=& \dfrac23 \cdot 6 \\\\ \mathbf{ x} & \mathbf{=} & \mathbf{4\ \text{pounds}} \\ \hline \end{array}\)

The least number of pounds of sugar that Betty could buy are \(\mathbf{4\ \text{pounds}}\).

heureka
Aug 29, 2018