PLEASE HELP?! (Math Word Problem)

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moralisaiah

March 30, 2019 17:50

Rob spent percent more time on his research project than he had planned. He spent an extra h hours on the project.

Which of the following expressions could represent the number of hours Rob (actually) spent on the project.

A. (h/0.25)1.25
B. 4h
C. 5h
D. 1.25h
E. (1+25/100)h

*I already know the answer (C,E) but I have a hard time knowing the steps to get to those answers, like for example, Khan Academy explains it by the following;

So my series of questions are:

1. How do you get h/25% in step one, like why divide?
2. In step 4, how do they get 5h to .25/.25(5h)?

3. Maybe someone can explain each step more thoroughly and why?

Would really appreciate the help, Thanks :)

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20leunge

April 02, 2019 22:38

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Here's how I see it.

Let x represent the time Rob intended to spend on the project. However, he spent 100% of that times AND 25% more, so 125% of the planned time. So the time Rob actually spent was 1.25*x. Subtracting a 1*x or simply x means subtracting the planned time, leaving us with the extra time. 1.25*x - x = 0.25*x = h.

Dividing both 0.25*x and h by 0.25, we get the equation (0.25/0.25)*x = h/0.25 ==> x = 4*h.

We want to multiply both sides by 1.25 so that we get 1.25*x, the actual time Rob spent on the project. On the right side of the equation, we get 1.25*4*h = 5h.

As you can see, we introduced another variable that (hopefully) makes the division by 0.25 more intuitive.

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PLEASE HELP?! (Math Word Problem)

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