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Ratio

by bia » Fri May 16, 2008 6:12 am
It sounds easy but i can't find the answer :-(

A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?
A 20
B 36
C 48
D 60
E 84
Bia
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by mandy12 » Fri May 16, 2008 7:01 am
is the answer 60 ?
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by bia » Fri May 16, 2008 7:12 am
C is answer
Bia
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by roy_priya » Fri May 16, 2008 9:59 am
A linear relation is represented by following equation:

y = mx + b

We are familiar with it in co-ordinate geometry, basically the R and S scale are the X and Y axes.

So: r = ms + b where m = slope and b is the intercept on r axis

We get two equations by substituting the numbers given:

60 = 30 m + b (1)

24 = 60 m + b (2)

Solving these 2 equations we get m = 3/5 and b = -12

So equation is r = 3/5 s -12

Substituting s = 100,

R = 48 (Answer - C)
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by AleksandrM » Fri May 16, 2008 10:06 am
6/30 = 1/5 and 24/60 = 2/5, so then number x over 90 = 3/5 and x = 54. This means that the next number over 100 will have to be a little lower than this. The best choice is 48.
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by beeparoo » Sat May 17, 2008 4:40 pm
roy_priya wrote:basically the R and S scale are the X and Y axes.
I give props to Roy for his clever analysis on that. Good job.
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by AleksandrM » Sat May 17, 2008 6:28 pm
I certainly agree with beeparoo, that was an excellent approach by roy. Way to use algebra.
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by smashinonions » Wed May 21, 2008 6:22 pm
I think the answer should be 60

Since R and S are linearly related, we can take them as X and Y cordinates

ie. X value (R) : x1 = 6 and x2= 24
and Y value (S): y1 = 30 and y2 = 60

so the slope of a line passing these point (X,Y) will be: y2 - y1 / x2 - x1

= 60-30/ 24-6 = 30/18 = 5 / 3

so new equation is: y = mx + c

y = 100, so x= y/m = 100 * 3 /5 = 60
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