Question

Koby can work about 22 math problems in 30 minutes. At this rate, how many math problems can Koby work in 3 hours?

Answer 1

`132color(white)(i)"math problems"`

Explanation:

`1`. Start by converting `3` hours into minutes.

`3color(white)(i)"hours"`

`=3color(white)(i)"hours"xx(60color(white)(i)"minutes")/"hour"`

`=3color(white)(i)color(red)cancelcolor(black)("hours")xx(60color(white)(i)"minutes")/color(red)cancelcolor(black)("hour")`

`=3xx60color(white)(i)"minutes"`

`=color(blue)(180color(white)(i)"minutes")`

`2`. Multiply `180color(white)(i)"minutes"` by `(22color(white)(i)"math problems")/(30color(white)(i)"minutes")`.

`color(blue)(180color(white)(i)"minutes")xx(22color(white)(i)"math problems")/(30color(white)(i)"minutes")`

`=180color(white)(i)color(red)cancelcolor(black)("minutes")xx(22color(white)(i)"math problems")/(30color(white)(i)color(red)cancelcolor(black)("minutes"))`

`=180xx(22color(white)(i)"math problems")/30`

`3`. Since `180` and `30` can be divided by a common factor, their values are reduced.

`=180color(red)(-:30)xx(22color(white)(i)"math problems")/(30color(red)(-:30))`

`=6xx(22color(white)(i)"math problems")/1`

`=color(green)(|bar(ul(color(white)(a/a)132color(white)(i)"math problems"color(white)(a/a)|)))`

Answer 2

132 problems

Explanation:

Instead of working with two different units of time, lets think in hours.

If Koby does 22 problems in 30 minutes (which is half an hour,)
then he will do 44 in one hour.

44 problems in 1 hour means in 3 hours he will do 3 times as many:
3 x 44 = 132 problems.

This can also be considered as a direct proportion question.
The more time he spends, the more problems he can do.

3 hours = 180 minutes

`22/30 = x/180`

`30x = 22 xx180`

`x = (22 xx1 80)/30`

`x = 132`