Question

You spend 100 minutes in 2 classes. Write a

proportion that gives the number m of minutes you spend in 3 classes.

Answer 1

Let's use the concept of proportion to find the number of minutes spent in 3 classes. We can set up a proportion using the fact that the ratio of time spent in two classes is equal to the ratio of time spent in three classes. Therefore, we can write:

`$\frac{\text{time spent in class 1}}{\text{time spent in class 2}} = \frac{\text{total time spent in 2 classes}}{\text{time spent in class 3}}$`

Let's substitute the given values:

`$\frac{\text{time spent in class 1}}{\text{time spent in class 2}} = \frac{100 \text{ minutes}}{m \text{ minutes}}$`

where m is the number of minutes spent in 3 classes.

Now we can cross-multiply to solve for m:

`$\text{time spent in class 1} * \text{time spent in class 3} = \text{time spent in class 2} * \text{total time spent in 2 classes}$`

Plugging in the given values:

`$\text{time spent in class 1} * m = \text{time spent in class 2} * 100 \text{ minutes}$`

We know that we spent 100 minutes in 2 classes, so we can substitute this value into the equation:

`$\text{time spent in class 1} * m = \text{time spent in class 2} * 100 \text{ minutes} =`
`\text{time spent in class 1} * (100 \text{ minutes} - \text{time spent in class 1})$`

Simplifying and rearranging the terms:

`$m \text{ minutes} = \frac{\text{time spent in class 1} * (100 \text{ minutes} - \text{time spent in class 1})}{\text{time spent in class 1}}$`

`$m \text{ minutes} = 100 \text{ minutes} - \text{time spent in class 1}$`

Therefore, the proportion that gives the number of minutes spent in 3 classes is:

`$\frac{\text{time spent in class 1}}{\text{time spent in class 2}} = \frac{100 \text{ minutes}}{m \text{ minutes}} =\large\boxed{ \frac{100 \text{ minutes} - m \text{ minutes}}{m \text{ minutes}}}$`