Question

Matias solved 28 math problems in 20 minutes yesterday. Using the same rate, how many math problems can Matias solve in 90 minutes?

Answer 1

Answer:

A handy technique I like to use for these type of problems is Dimensional Analysis.

Basically the way it works is you create conversion factors between units and multiply and cancel out units.

You start by setting up an equality.

In this case the equality is 28 math problems = 20 minutes.

To get a conversion factor from this equation, you have to move all terms onto one side so that the other side is 1.

To do this, you divide both sides by 20 minutes.

This leaves you with:

28 math problems / 20 minutes = 20 minutes / 20 minutes

On the right side, you can see that 20 minutes / 20 minutes is just equal to one. And on the left side you separate the numbers and units to get 28/20 math problems/ minute.

28/20 is equal to 1.4 and math problems / minute can be interpreted as math problems per minute.

So we now know that Matias can do 1.4 math problems/min or 1.4 math problems per minute.

To find how many math problems he can do in 90 minutes you have to multiply the conversion factor(1.4) by the number of minutes (90) so that the minutes cancel out and you are left with math problems.

so:

90 minutes * 1.4 math problems / minutes = 90*1.4 math problems * minutes / minutes

minutes/minutes is just equal to one, so the answer is 126 math problems.

Hope that helped :)

Answer 2

Answer:

she can solve 84 math problems in 90 minutes, because 20 minutes x 3 = 90 minutes. so 28 x 3 = 84