Lesson: Introduction to Algebra

If x is the number on the number line between 5 and 15 that is twice as far from 5 as from 15, then x is

so i got 3x = 10 and x = 10/3 but why do we have to do this: 5+2x=5+20/3=35/3

or 15−x=15−10/3=35/3=11 2/3

I received this question from a Magoosh study and wanted to see whats the easiest way to approach it:

The Sargon Corporation offers an optional stock-option buy in program to its employees. Of the employees with salaries greater than or equal to $100K, 85% choose to participate in this plan. Of the employees with salaries less than $100K, 77% choose to participate in this plan. Which of the following could be the total number of employees? Answer choices below:

100
200
350
460
525
640
750
880

For this question what I specifically did was convert that 85(x)/100 , where is the total people who went with the plan into 17(x)/20 and same thing for the 77(x)/100. I then looked at the choices and broke each answer choice in half so for 200 it would become 100 and 100 and plugged this into the equation 17(x)/20 and 77(x)/100 to see if they would work. I did this for each answer choice and got only 200 and 640 as the answers but the complete list of answers are 200,460,640, and 880. Also please clarify if my approach is right for could be problems: As a could be problem if we find one answer choice that works then we would select that choice. But does this also mean we may run into conditions that don't work, but yet that answer choice may still be correct. For example in this problem I thought 460 does not work since I break it down into 230 and 230 even it did not go evenly into the fractions, but yet it is a correct answer.

https://gmatclub.com/forum/in-an-electric-circuit-two-resistors-with-resistances-x-and-144899.html

For this question I solved it via algebra and got answer choice D xy /(y+x), my question is however on the answer choices, like why cant someone choose r = x+y and get it right as well?

Thanks very much.. I find very interesting and useful materials here. Well done!