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(2)/(16)=(3)/(1)\cdot(2)/(16)=(6)/(16)`

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

`(1)/(2)\cdot(6)/(16)=(6)/(32)=(2\cdot3)/(2\cdot16)=(3)/(16)`

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

`(3)/(16)-(1)/(16)=(2)/(16)`

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

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

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