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October 1st, 2018, 09:35 PM  #1 
Member Joined: Sep 2018 From: Japan Posts: 35 Thanks: 2  Height of two plants
The height of two plants is in the ratio 7:9. the height of the taller plant is 26 cm more than the height of the shorter plant. What is their total height? My work: (I'm not sure if I'm making math up) Height of plant 1: P1 Height of plant 2: P2 Changing the ratio to fraction, I got this: P1 = 7/16 and P2 = 9/16 We know the height of the taller plant is 26cm more than the height of the shorter plant. So, P2 = P1 + 26 Below is the part where I'm not sure if I did it mathematically correct. (P1/P2) = 7/9 We know P2 = P1 + 26 9P1 = 7P2 9P1 = 7(P1 + 26) P1 = 13. Then I used the ratio 7:9. But I'm guessing we can write 7:9 to this: 7k:9K because we don't know the height. then we can change P1 = 13 to k = 13. So 7(13) + 9(13) = 208 
October 1st, 2018, 11:02 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,113 Thanks: 2327 
Solving 9P1 = 7(P1 + 26) gives P1 = 91 (not 13), so P2 = 91 + 26 = 117 and P1 + P2 = 208.

October 2nd, 2018, 12:13 AM  #3 
Member Joined: Sep 2018 From: Japan Posts: 35 Thanks: 2  opps  (P1/P2) = 7/9 We know P2 = P1 + 26 9P1 = 7P2 9P1 = 7(P1 + 26) P1 = 91. From my work, besides the mistake. Is it mathematically correct? Is there a better way to do this word problem? 
October 2nd, 2018, 06:56 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,113 Thanks: 2327 
Apart from the mistake, you were essentially correct. You should state that P1 = 7/16 and P2 = 9/16 are both fractions of the total height. You can then deduce that their difference is 2/16 of their total. The difference (as a specific value, not a ratio) is given as 26, so the total is 26/(2/16) = 208. 
October 2nd, 2018, 09:11 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 
On a timed test, you wanna go as fast as possible: u = shorter plant u/(u+26) = 7/9 Do a crisscross multiplication and you're almost finished... 

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