Question

Some students are working together to draw a picture of a playground.

Answer 1

From the information provided by the statement, you know that

*Ann draws 2/16 of the playground

*Susan draws 6/16 of the playground because she draws 3 times as much as Ann so

$3\cdot\frac{2}{16}=\frac{3}{1}\cdot\frac{2}{16}=\frac{6}{16}$

*Louise draws 3/16 because she draws half as much as Susan, so

$\frac{1}{2}\cdot\frac{6}{16}=\frac{6}{32}=\frac{2\cdot3}{2\cdot16}=\frac{3}{16}$

*Sam draws 2/16 because she draws 1 less section than Louise

$\frac{3}{16}-\frac{1}{16}=\frac{2}{16}$

Now, let x be the fraction of the playground that still needs to be drawn. Then, you have

$\begin{gathered} \frac{2}{16}+\frac{6}{16}+\frac{3}{16}+\frac{2}{16}+x=\frac{16}{16} \\ \text{ Add similar terms} \\ \frac{13}{16}+x=\frac{16}{16} \\ \text{ Subtract }\frac{13}{16}\text{from both sides of the equation} \\ \frac{13}{16}-\frac{13}{16}+x=\frac{16}{16}-\frac{13}{16} \\ x=\frac{3}{16} \end{gathered}$

Therefore, 3/16 of the playground still needs to be drawn.