Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 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. Thanks from xoritos October 2nd, 2018, 12:13 AM   #3
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Quote:
 Originally Posted by skipjack Solving 9P1 = 7(P1 + 26) gives P1 = 91 (not 13)
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. Thanks from xoritos 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 criss-cross multiplication and you're almost finished... Thanks from xoritos Tags height, plants Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Neel Trigonometry 3 November 6th, 2016 12:39 PM Neel Trigonometry 7 November 5th, 2016 04:39 AM girlbadatmath Chemistry 3 November 24th, 2014 02:38 AM rakmo Algebra 3 March 28th, 2013 06:20 AM symmetry Algebra 3 July 26th, 2007 02:01 PM

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