Question

Wilson paints 40% of a bookcase in 20 minutes.How much more time will it take him to finish the bookcase?1. Write an equation using equal fractions to represent this situation. Use a box to represent the time it takes to paint the whole bookcase. 2 Use your equation to find the amount of time it will take Wilson to paint the whole bookcase. Explain how you found this answer. 3. How much time will it take Wilson to finish painting the bookcase? Explain.

Answer 1

`\begin{gathered} 1)(2)/(5)x=(3)/(5)\cdot20 \\ 2)50\min \\ 3)30\min \end{gathered}`

We can start that, by rewriting 40% as a fraction:

`(40)/(100)=(2)/(5)`

So let's find how long it will take to finish this painting, by writing the following fractions, and from them an equation:

1)

`\begin{gathered} (2)/(5)---20 \\ (3)/(5)---x \\ (2)/(5)x=(3)/(5)\cdot20 \\ (2)/(5)x=12 \end{gathered}`

So this is the equation, let's find the time to complete the painting:

`\begin{gathered} (2)/(5)x=12 \\ 5*(2)/(5)x=12*5 \\ 2x=60 \\ (2x)/(2)=(60)/(2) \\ x=30 \end{gathered}`

So it will take plus 30 minutes for to Wilson finish the bookcase. Note that

5/5 is equivalent to the whole bookcase or 100%

2) The amount of time to paint this whole bookcase, is found taking the initial 20 minutes and adding to them the 30 minutes we can state that the painting overall takes 50 minutes

3) Sorting out the answers:

`\begin{gathered} 1)(2)/(5)x=(3)/(5)\cdot20 \\ 2)50\min \\ 3)30\min \end{gathered}`