Difference between revisions of "2017 AMC 10B Problems/Problem 4"
m (→Solution) |
m (→Solution 1) |
||
| Line 7: | Line 7: | ||
===Solution 1=== | ===Solution 1=== | ||
| − | Rearranging, we find <math>3x+y=-2x+6y</math>, or <math>5x=5y\implies x=y</math> | + | Rearranging, we find <math>3x+y=-2x+6y</math>, or <math>5x=5y\implies x=y</math>. |
Substituting, we can convert the second equation into <math>\frac{x+3x}{3x-x}=\frac{4x}{2x}=\boxed{\textbf{(D)}\ 2}</math>. | Substituting, we can convert the second equation into <math>\frac{x+3x}{3x-x}=\frac{4x}{2x}=\boxed{\textbf{(D)}\ 2}</math>. | ||
Revision as of 10:11, 26 July 2017
Contents
Problem
Supposed that 
and 
are nonzero real numbers such that 
. What is the value of 
?
Solution
Solution 1
Rearranging, we find 
, or 
.
Substituting, we can convert the second equation into 
.
Solution 2
Substituting each and with 
, we see that the given equation holds true, as 
. Thus, 
| 2017 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
