Do I have a problem? Basic proportion problem.

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The discussion revolves around a basic math problem involving proportions, where the participant compares their solution method to that of a textbook. They solved the problem using a more complex approach, while the book used a simpler method, leading to concerns about potential complications in future math courses. The participant has a strong academic background and is worried that their preference for complexity might hinder their performance in engineering. Ultimately, the consensus is that both methods yield the correct answer, and as long as the participant understands the concepts, they should be fine. The focus remains on mastering proportional reasoning for future studies.
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Hello, this is an odd question but when I compared how I solved it compared to how the book solved it I kinda got worried. It was a very basic problem I been going back and touching up on my basics before I start pre-cal and trig in college.

The problem was: After completing 7/10 of his math homework assignment, Josh has 15 more questions complete. What is the total number of questions on his assignment? The answer was 50.

I got that by

\frac{7}{10}=\frac{(x-15)}{x} Followed by cross multiplying and dividing.

However the book does it simply by doing the subtraction 10-7 = 3 then setting it up as

\frac{3}{10}=\frac{15}{x} Then cross multiply and divide.

I know someone will say "It works so you can do what you are doing". But is there a possibility this kind of over complication( haha not hardly complicated!) Can hurt me later on? The way I performed it seemed much more intuitive... I have a high school record of up to ap calc and ap chem and I'm worried if I pursue engineering in college I'll have a hard time solving simple things because of my use to complexity?
 
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(3/10)x=15
x=50
 
Life-Like said:
Hello, this is an odd question but when I compared how I solved it compared to how the book solved it I kinda got worried. It was a very basic problem I been going back and touching up on my basics before I start pre-cal and trig in college.

The problem was: After completing 7/10 of his math homework assignment, Josh has 15 more questions complete.
Do you meant "15 more questions to complete"? What you wrote could be interpreted as meaning has completed 15 questions. If he has already completed 7/10 of his assignment, he still has 3/10 left. If he has 15 questions more to complete, letting "x" be the total number of problems, (3/10)x= 15 so x= (10/3)(15)= 150/3= 50.

What is the total number of questions on his assignment? The answer was 50.

I got that by

\frac{7}{10}=\frac{(x-15)}{x} Followed by cross multiplying and dividing.

However the book does it simply by doing the subtraction 10-7 = 3
Okay, that is, they are calculating 1- 7/10= 10/10- 7/10= (10- 7)/10= 3/10 as I did.

then setting it up as

\frac{3}{10}=\frac{15}{x} Then cross multiply and divide.

I know someone will say "It works so you can do what you are doing". But is there a possibility this kind of over complication( haha not hardly complicated!) Can hurt me later on? The way I performed it seemed much more intuitive... I have a high school record of up to ap calc and ap chem and I'm worried if I pursue engineering in college I'll have a hard time solving simple things because of my use to complexity?
As long as you have linear problems, you can set them up as "proportions" and get the correct answer.

 
Thanks guys
 
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