Question

When making pancakes, the amount pancake mix varies directly with the number of pancakes made. If 2 cups of min Produces 13 pancakes, how many pancakes would be produce with 12 cups of pancake mix?

Answer 1

Total count of pancakes made with 12 cups is 78

Explanation:

The wording of this question indicates that they are looking for something very specific.

As soon as you see the word 'varies' in this question type you are looking for:

answer= (constant of variation) x (some value)

In this case the constant of variation is "the number of pancakes made from 1 cup measure"

Let the constant of variation be `k` giving

`"Total count of pancakes "= k xx" count of cups"`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given that 2 cups makes 13 pancakes then 1 cup makes `13/2` pancakes. So `k=13/2`

Let the total count of pancakes be `y`
Let the count of cup measures be `x`

Then `y=kx" "->" "y=13/2 x`

We are told that the number of cups used is 12 so `x` is `12` giving:

`y=13/2xx12" "->" "y=13/(cancel(2)^1)xx cancel(12)^6`

`y=13xx6 =78`

Total count of pancakes made with 12 cups is 78
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Tip about calculating "13xx6" without a calculator")`

13 can be split into `10+3`

So `13xx6" " ->" " 6xx(10+3)`

`6xx10 = 60`
`ul(6xxcolor(white)(1)3=18) larr" Add the 60 and 18"`
`color(white)(6xx10 =) 78`