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Scaling up from a Numerator and Denominator to a Triple Ratio

Date: 07/08/2011 at 07:56:38
From: Jon
Subject: Ratio and Proportion

The ratio of mango trees to guava trees to apple trees in an orchard is
4:3:5. If there are 960 trees in the orchard, how many of each kind of
tree are there?

   a. 320; 240; 400
   b. 120; 240; 360
   c. 240; 360; 480
   d. 120; 280; 340
   e. 20; 40; 60

Fractions typically consist of only two parts, but this problem presents
three unknowns in proportion with one another.

I've tried

   number of mango trees = 960/4 = 240
   number of guava trees = 960/3 = 320
   number of apple trees = 960/5 = 192

But this answer is not one of the choices given.

Please help on how to solve this.



Date: 07/08/2011 at 08:20:33
From: Doctor Jerry
Subject: Re: Ratio and Proportion

Hello Jon,

Thanks for writing to Dr. Math.

We know that 

   m:g:a = 4:3:5

According to what "triple ratios" mean, this is equivalent to some
constant, k, equaling

   m/4 = g/3 = a/5

So,

   m = 4k
   g = 3k
   a = 5k

Then,

   4k + 3k + 5k = 960 

            12k = 960

              k = 80

Now, m = 4*k = 320 and so on.

Please feel free to write back -- using the URLs at the bottom of this
message -- if you have questions relative to my comments.

- Doctor Jerry, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
Middle School Ratio and Proportion

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