Question

Nasane can do 50 sit-ups in 3 minutes. At this rate, how many can he do in 12 minutes?

Answer 1

200 in 2 minutes

Explanation:

This problem can be set out as a fraction in ratio form.

Where x represents the number of sit-ups in 12 minutes.

`color(red)(3)/color(blue)(50)=color(blue)(12)/color(red)(x)`

Using cross-multiplication. That is, multiply the`color(red)" red"` values and the `color(blue)"blue"` values and equate them.

`rArrcolor(red)(3x)=color(blue)(12)xxcolor(blue)(50)`

`rArr3x=600`

To solve for x, divide both sides of the equation by 3

`(cancel(3) x)/cancel(3)=600/3`

`rArrx=200`

Thus, Nasane can do 200 sit-ups in 12 minutes.

Answer 2

The sit up count for 12 minutes is 200

Explanation:

Similar to Jim's solution
Assumption: The rate of sit-ups is constant

Let the unknown count of sit-ups be `x`

Using ratio

`("sit-up count")/("time")->50/3 -=x/12`

Jim cross multiplied at this point.

To change the 3 from `50/3` into 12 we multiply by 4

Multiply a number or fraction by 1 and you do not change its value. However 1 comes in many forms

`color(green)([50/3color(red)(xx1)] " "->" "[50/3color(red)(xx4/4)] = 200/12-=("sit-up count")/("time")`

So the sit up count for 12 minutes is 200
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The reality is that the rate of sit ups could well change. As time progresses Nasan would find it harder and harder so he would slow down. Unless he is very fit that is.