June 15th, 2014, 10:14 PM  #1 
Member Joined: Jun 2014 From: pennsylvania Posts: 45 Thanks: 0  Help me understand this problem. Hello, I just wanted some help on how to answer this type of question, I don't understand what I have to do. The 37 1/2 & 2 2/3 is what I guessed. I also wanted to know how to solve this one because I was only able to get so far before not being sure what to do, and the answer that I was supposed to choose from, I was unable to extrapolate from the equation. The last step I got to before I did not know what to do further was 15ax1 divide by 5 Last edited by skipjack; June 17th, 2014 at 12:14 AM. 
June 15th, 2014, 10:46 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,514 Thanks: 2515 Math Focus: Mainly analysis and algebra 
For the first one, you have the scale correct, but not the height. The bridge is 44 feet long, and on the diagram it is 16.5 inches. So we have 16.5 inches represents 44 feet. So how many inches represent 1 foot? Well, if we divide by 44 we get $\frac{16.5}{44} = 2 \frac{2}{3}$ inches represent $\frac{44}{44} = 1$ foot. We can do a similar thing in reverse for the height. We have 1 foot is represented by $2 \frac{2}{3} = \frac{8}{3}$ inches. We want 10 feet, so let's multiply by 10. Then 10 feet are represented by $10 \cdot \frac{8}{3}$ inches. For the second one you have $$3ax = \frac{1}{5}$$ So $x$ is multiplied by something: what? To isolate the $x$, we therefore divide both sides of the equation by that something. Last edited by skipjack; June 17th, 2014 at 12:11 AM. 
June 16th, 2014, 12:03 AM  #3 
Member Joined: Jun 2014 From: pennsylvania Posts: 45 Thanks: 0 
Thanks again v8 for giving me the time. First off I'm glad I got the scale right. But redoing it just now, I'm not sure on something. When I divide 16.5 by 44, I get 0.304 and if I turn that into a fraction I don't think I can turn it into the 2 2/3. And the last part I understand now, it was 26 2/3. I just need to exactly understand how we get that 2 2/3 scale? I'm sorry if I'm not understanding your answer to the second problem I had, but if you can elaborate a bit more I would appreciate it even more Last edited by skipjack; June 17th, 2014 at 12:16 AM. 
June 16th, 2014, 09:47 PM  #4 
Member Joined: Jun 2014 From: pennsylvania Posts: 45 Thanks: 0 
Sorry about my past post, everything checks out and you helped me solve the scale type of problem I might encounter again. But I still want to understand the other question so if you could please explain it to me. Thank you. Last edited by skipjack; June 17th, 2014 at 12:16 AM. 
June 17th, 2014, 12:52 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,992 Thanks: 1855 
There are mistakes in the above. As 16.5 in. represents 44ft, 3/8 in. represents 1 ft, and so 3 3/4 in. represents 10 ft. Thus 3 3/4 should have been dragged to the height box and 3/8 should have been dragged to the Scale box. To solve 3ax = 1/5, divide both sides by 3a. That gives x = 1/(15a), which is choice A. 
June 17th, 2014, 05:58 AM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,514 Thanks: 2515 Math Focus: Mainly analysis and algebra 
There are plenty of mistakes in my first post. I apologise. I'll look at it again later.

June 17th, 2014, 09:43 AM  #7 
Member Joined: Jun 2014 From: pennsylvania Posts: 45 Thanks: 0 
Thanks skipjack for the correction. I want to make sure I get this 100%. Ok, I really wanna figure this out. I guess I was trying to solve it differently? I got stuck on 15ax1 divide by 5 If I do it the way you mention, can you please show me how I divide 3a into 1/5. If I divide 3a into 3ax, am I not left with 1x? I'm not sure how to divide the 3a into the 1/5. Can you guys please explain the first problem to me? I'm not getting 3/8 in my calculations. When I was explained, it was 2 2/3; I was able to get that calculation. So please tell me what needs to be corrected, and what to do so I can understand. Thanks Last edited by skipjack; June 18th, 2014 at 01:01 PM. 
June 18th, 2014, 01:13 AM  #8 
Member Joined: Jun 2014 From: pennsylvania Posts: 45 Thanks: 0 
~bump

June 18th, 2014, 03:40 AM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,638 Thanks: 954 
RULE: (a/b) / (c/d) = (a/b) * (d/c) = (ad) / (bc) : you knew that, right? (1/5) / (3a/1) = (1/5) * (1/(3a)) = 1 / (15a) .... slap your forehead !! 
June 18th, 2014, 01:21 PM  #10 
Global Moderator Joined: Dec 2006 Posts: 19,992 Thanks: 1855 
In the first problem, 16.5in. represents 44ft, so (16.5/44)in. represents 1ft. To evaluate 16.5/44, I first doubled the numerator and denominator to get 33/88, then I divided the numerator and denominator by 11 to get 3/8. Thus (3/8)in. represents 1ft, and so (30/8)in. represents 10ft. As 30/8 = 3 3/4, that means (3 3/4)in. represents 10ft. In the second problem, dividing 3ax by 3a gives x. Dividing 1/5 by 3a is done by multiplying 1/5 by 1/(3a). $$\frac15 / (3a) = \frac15 \times \frac{1}{3a} = \frac{1 \times 1}{5 \times 3a} = \frac{1}{15a}$$ 

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