Question Video: Representing Proportional Relationships by Equations Mathematics • 6th Grade

Holly paints one garden chair in 12 minutes. Write an equation for the number of chairs 𝑐 that she could paint in β„Ž hours.

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Video Transcript

Holly paints one garden chair in 12 minutes. Write an equation for the number of chairs 𝑐 that she could paint in β„Ž-hours.

We are told in this question that Holly can paint one chair in 12 minutes. However, we’re interested in the number of chairs that she can paint in β„Ž-hours. Let’s firstly consider how many chairs Holly could paint in one hour. We know that 60 minutes is equal to one hour. We need to work out the number of chairs that can be painted in 60 minutes.

We could begin to count up in twelves. Holly would be able to paint two chairs in 24 minutes as 12 plus 12 is 24. Adding another 12 gives us 36 minutes. So she can paint three chairs in this time. Holly could paint four chairs in 48 minutes and five chairs in 60 minutes. You might however have noticed immediately that 12 multiplied by five is equal to 60. Either way, we can see that Holly can paint five chairs in 60 minutes or one hour.

We now need to write an equation for the number of chairs 𝑐 that she can paint in β„Ž-hours. If Holly can paint five chairs in one hour, she could paint 10 chairs in two hours, 15 chairs in three hours, and so on. In β„Ž-hours, she would be able to paint five β„Ž or five multiplied by β„Ž chairs. Our equation is therefore 𝑐 is equal to five β„Ž. We could then substitute in values for β„Ž and 𝑐. We could substitute in values for β„Ž to work out the number of chairs painted in a certain number of hours or substitute in a value for 𝑐 to work out the number of hours it would take to paint a certain amount of chairs.

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