## ValentinaT 2 years ago Help please? With steps?

1. ValentinaT

2. e.mccormick

How far did you get with this?

3. ValentinaT

Hold on a second please, I'm writing.

4. e.mccormick

Kk. Cause I do have a path to the answer...

5. ValentinaT

$\frac{ 72 }{ 2 } + \frac{ 72 }{ x } = \frac{ 72 }{ 1.5 }?$

6. e.mccormick

hmm... I can see where you got the 72/2 and 72/1.5.... but the 72/x makes no sense to me.

7. ValentinaT

Sorry, I was looking at the example in my book, and tried to model it like it.

8. e.mccormick

$$c_1 cpm=\frac{72}{2}$$ and $$c_2 cpm=?$$ Where cpm is Copies Per Minute $$1.5(c_1 cpm+c_2 cpm)=72$$

9. e.mccormick

Once you know the CPM for the old copier, you can find out how long it takes to make 72 copies.

10. ValentinaT

Sorry, I was writing this down.

11. e.mccormick

Your method might actually do that in one shot, don't know. You could run it both ways and see.

12. ValentinaT

How do I find the cpm for the old copier? $1.5(\frac{ 72 }{ 2 } + \frac{ 72 }{ x }) = 72$?

13. e.mccormick

You just need x. Not 72/x.

14. ValentinaT

Okay. $1.5(\frac{ 72 }{ 2 } + x) = 72$

15. ValentinaT

Can you give me a hint on what to do next?

16. e.mccormick

Move the 1.5 to the other side, do the dractions. They become nice numbers.

17. e.mccormick

fractions... oops. I was checking the other way. It would get a very bad number.

18. ValentinaT

Okay. $\frac{ 15 }{ 10 } (\frac{ 72 }{ 2 } + x) = 72$ End up with 12.

19. e.mccormick

My version of the work:$1.5\left(\frac{ 72 }{ 2 } + x\right) = 72 \\ \implies \frac{ 72 }{ 2 } + x = \frac{72}{1.5} \\ \implies 36 + x = 48 \\ \implies x = 48-36 \\ \implies x = 12$So 12 copies per minute. Then the time for 72 copies is $$\frac{72}{12}$$

20. ValentinaT

Okay, thank you.

21. e.mccormick

Yah, these and riverboat problems are all about finding what is added and what is multiplied. The true goal of word problems is trying to help you figure out how math works in real life rather than just in homework.

22. ValentinaT

Okay, 6 minutes.

23. e.mccormick

/cheer Yep. Really slow copier.

24. ValentinaT

Haha.