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October 1st, 2018, 08:35 PM   #1
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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
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October 1st, 2018, 10:02 PM   #2
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Solving 9P1 = 7(P1 + 26) gives P1 = 91 (not 13), so P2 = 91 + 26 = 117 and P1 + P2 = 208.
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October 1st, 2018, 11:13 PM   #3
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Quote:
Originally Posted by skipjack View Post
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?
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October 2nd, 2018, 05:56 AM   #4
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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.
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October 2nd, 2018, 08:11 AM   #5
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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...
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