Question

Jessica is a professional baker. She bakes 113 cupcakes in 2 hours How many cupcakes will she make in 6 hours? Jessica can make cupcakes in 6 hours How long will it take her to make 791 cupcakes? It will take Jessica 791 cupcakes hours to make The equation that represents this situation is y Time (hour) Cupcakes 113 2 791

Answer 1

You know that Jessica can bake 113 cupcakes in 2hours, using this relationship you can calculate the number of cupcakes she can bake in 6 hours using cross multiplication:

2hours_____113cupcakes

6hours_____xcupcackes

$\begin{gathered} \frac{113}{2}=\frac{x}{6} \\ (\frac{113}{2})\cdot6=x \\ 339=x \end{gathered}$

She can bake 339 cupcakes in 6 hours.

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To determine how much time it will take to make 791 cupcakes you can also apply cross multiplication, this time you know the amounts of cupcakes and neet to calculate the time:

So if the can make 113 cupcakes in 2 hours,

Then she will make 791 cupcakes in x hours:

113 cupcakes_____2hours

791 cupcakes_____xhours

$\begin{gathered} \frac{2}{113}=\frac{x}{791} \\ (\frac{2}{113})\cdot791=x \\ 14=x \end{gathered}$

It will take her 14 hours to make 791 cupcakes.

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To determine an equation that represents this situation, first determine the variables.

In this case:

y → will represent the number of cupcakes made

x → will represent the time she spent coocking the cupcakes

Next is to determine how many cupcakes she makes in one hour:

If she makes 113 cupcakes in 2hours, in half the time she will make half the cupcakes, that is

$\frac{113}{2}=56.5$

She makes 56.5 cupcakes per hour, since each passing hour se adds 56.5 cupcakes then this number will represent the coefficient of variation (or slope) of the equation and must multiply x.

Then the equation that represents this relationship is

$y=56.5x$