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Least: (R-2x-y)/3
Greatest: (R+x+2y)/3
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The real number R is expressed as the sum of three numbers so that the median of the three numbers is x greater than the least of the three numbers and y less than the greatest of the three numbers, where x and y are positive real numbers. Select for Least an expression equivalent to the least of the three numbers and select the Greatest an expression equivalent to the greatest of the three numbers. Make only two selectionA, one in each column.
| Least | Greatest | |
| (R-2x-y)/3 | ||
| (R-x-2y)/3 | ||
| (R-x-y)/3 | ||
| (R+x+y)/3 | ||
| (R+x+2y)/3 | ||
| (R+2x+y)/3 |
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Least: (R-2x-y)/3
Greatest: (R+x+2y)/3
24 Jan 2024, 10:01
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gmatt1476
The real number R is expressed as the sum of three numbers so that the median of the three numbers is x greater than the least of the three numbers and y less than the greatest of the three numbers, where x and y are positive real numbers. Select for Least an expression equivalent to the least of the three numbers and select the Greatest an expression equivalent to the greatest of the three numbers. Make only two selectionA, one in each column.
The three numbers are a, b and c.Given : b=a+x and c=a+x+y
R= a+a+x+a+x+y = 3a+2x+y
\(a=\frac{R-2x-y}{3}\)...a is the least.
Greatest = a+x+y = \( \frac{R-2x-y}{3}+x+y= \frac{R-2x-y+3x+3y}{3}=\frac{R+x+2y}{3}\)...
22 Sep 2024, 11:53
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shwetasood
chetan2u
gmatt1476
The real number R is expressed as the sum of three numbers so that the median of the three numbers is x greater than the least of the three numbers and y less than the greatest of the three numbers, where x and y are positive real numbers. Select for Least an expression equivalent to the least of the three numbers and select the Greatest an expression equivalent to the greatest of the three numbers. Make only two selectionA, one in each column.
The three numbers are a, b and c.Given : b=a+x and c=a+x+y
R= a+a+x+a+x+y = 3a+2x+y
\(a=\frac{R-2x-y}{3}\)...a is the least.
Greatest = a+x+y = \( \frac{R-2x-y}{3}+x+y= \frac{R-2x-y+3x+3y}{3}=\frac{R+x+2y}{3}\)...
Can you please elaborate a bit? Its really difficult for me to translate the question stem to actual equations and i get lost in between especially in this question its really confusing
2. The numbers can be drawn on a number line.
3. Now we can write the distances between each other.
4. Since R = a + b + c, it equals the sum of the distances to 0.
5. So, R = (a) + (a + x) + (a + x + y) = 3a + 2x + y \(\rightarrow\) a = \(\frac{R - 2x - y}{3}\). In addition, R = (c - y - x) + (c - y) + (c) = 3c - 2y - x \(\rightarrow\) c = \(\frac{R + 2y + x}{3}\).
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