Difference between revisions of "2022 AMC 8 Problems/Problem 6"
MRENTHUSIASM (talk | contribs) |
MRENTHUSIASM (talk | contribs) |
||
| Line 6: | Line 6: | ||
==Solution== | ==Solution== | ||
| + | |||
| + | Let the smallest number be <math>x.</math> It follows that the largest number is <math>4x.</math> | ||
| + | |||
| + | Since <math>x,15,</math> and <math>4x</math> are equally spaced on a number line, we have | ||
| + | <cmath>\begin{align*} | ||
| + | 4x-15 &= 15-x \\ | ||
| + | 5x &= 30 \\ | ||
| + | x &= \boxed{\textbf{(C) } 6}. | ||
| + | \end{align*}</cmath> | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2022|num-b=5|num-a=7}} | {{AMC8 box|year=2022|num-b=5|num-a=7}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 10:38, 28 January 2022
Problem
Three positive integers are equally spaced on a number line. The middle number is 
and the largest number is 
times the smallest number. What is the smallest of these three numbers?
Solution
Let the smallest number be 
It follows that the largest number is 
Since 
and 
are equally spaced on a number line, we have
See Also
| 2022 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
