How to find X, knowing the rate of change between two numbers?

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TheCosmicBird

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Aug 19, 2021
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Hi,

I'm prepping for an interview, and was asked this math question and was stumped on how to approach it:

In Data Set 1, it took 177 minutes in total for Software A to analyze 12 files and Software B to analyze 15 files.
In Data Set 2, it took 633 minutes in total for Software A to analyze 60 files and Software B to analyze 39 files.

Using the above, in Data Set 3, how many minutes will it take in total for Software A to analyze 25 files and Software B to analyze 34 files?

It seems after finding the rate of change, I would somehow use proportions to find X, but I'm getting stumped on the specifics of how to approach this problem to find X.

I sincerely appreciate any insight anyone can provide.

Thank you!
~Cosmic
 
You need to assume Software A takes a constant amount of time to analyse a file, and same for Software B.

Let "a" be the amount of time Software A takes to analyse a file.
Let "b" be the amount of time Software B takes to analyse a file.

Can you form and equation for "In Data Set 1, it took 177 minutes in total for Software A to analyze 12 files and Software B to analyze 15 files."?
And do the same for the other piece of info you are given.

Solve simultaneously for "a" and "b".

Then you can answer the question.
 
Hi Harry,

Thank you for the tip, that makes sense. So using what you said, an equation I would make for both data sets is:

12a + 15b = 177
60a + 39b = 633

With "a" being the time it takes to Software A to analyze a file and "b" being the amount of time Software B takes to analyze a file. And if I were able to solve for "a" and "b", then I could easily solve the answer for Data Set 3 with the equation:

25a + 34b = X minutes.

So, the concept makes complete sense to me...I'm just stumped on the actual specifics of how to approach the math on this. In other words haha, I understand "what" I have to do and "why" I have to do it...I'm unsure of the "how".

Thank you again for taking the time to engage with a complete stranger on this! :D
~Cosmic
 
TheCosmicBird said:
Hi Harry,

Thank you for the tip, that makes sense. So using what you said, an equation I would make for both data sets is:

12a + 15b = 177
60a + 39b = 633

With "a" being the time it takes to Software A to analyze a file and "b" being the amount of time Software B takes to analyze a file. And if I were able to solve for "a" and "b", then I could easily solve the answer for Data Set 3 with the equation:

25a + 34b = X minutes.

So, the concept makes complete sense to me...I'm just stumped on the actual specifics of how to approach the math on this. In other words haha, I understand "what" I have to do and "why" I have to do it...I'm unsure of the "how".

Thank you again for taking the time to engage with a complete stranger on this! :D
~Cosmic
Click to expand...
Do a google search for:

solution of two linear equations and two unknowns​
​
You'll find millions of websites ready to help you - with videos.
 
Ah that's exactly what I needed, thanks Khan! Ok, googled "solution of two linear equations and two unknowns" and was able to figure out the answer. It's 388 minutes. Thanks again!
 
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