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lisabon 2012 [21]
3 years ago
14

Six people are standing in line for concert tickets. Their average age is 27. the average age of the first four people in line i

s 23. The average age of the last three people is 34. How old is the fourth person in line?
Mathematics
1 answer:
Vanyuwa [196]3 years ago
6 0
Total age 
<span>6 * 27 </span>
<span>162 </span>

<span>Subtotal age of first 4 </span>
<span>4 * 23 </span>
<span>92 </span>

<span>Subtotal of last 3 </span>
<span>3 * 34 </span>
<span>102 </span>

<span>In the total of the first 4 and last 3 </span>
<span>the 4th person has been counted twice. </span>
<span>This second time must be subtracted. </span>

<span>Therefor </span>
<span>92 + 102 - x = 162 </span>
<span>194 - x = 162 </span>

<span>Subtract 194 from both sides </span>
<span>-x = -32 </span>

<span>Multiply both sides by -1 </span>
<span>x = 32 

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.
</span>
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\bf \textit{equation of a circle}\\\\ &#10;(x- h)^2+(y- k)^2= r^2&#10;\qquad &#10;center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad &#10;radius=\stackrel{}{ r}\\\\&#10;-------------------------------\\\\&#10;(x+1)^2+y^2=36\implies [x-(\stackrel{h}{-1})]^2+[y-\stackrel{k}{0}]^2=\stackrel{r}{6^2}~~~~&#10;\begin{cases}&#10;\stackrel{center}{(-1,0)}\\&#10;\stackrel{radius}{6}&#10;\end{cases}

so, that's the equation of the circle, and that's its center, any point "ON" the circle, namely on its circumference, will have a distance to the center of 6 units, since that's the radius.

\bf ~~~~~~~~~~~~\textit{distance between 2 points}&#10;\\\\&#10;(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad &#10;A(\stackrel{x_2}{-1}~,~\stackrel{y_2}{1})\qquad \qquad &#10;%  distance value&#10;d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}&#10;\\\\\\&#10;\stackrel{distance}{d}=\sqrt{[-1-(-1)]^2+(1-0)^2}\implies d=\sqrt{(-1+1)^2+1^2}&#10;\\\\\\&#10;d=\sqrt{0+1}\implies d=1

well, the distance from the center to A is 1, namely is "inside the circle".

\bf ~~~~~~~~~~~~\textit{distance between 2 points}&#10;\\\\&#10;(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad &#10;B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{6})\\\\\\&#10;\stackrel{distance}{d}=\sqrt{[-1-(-1)]^2+(6-0)^2}\implies d=\sqrt{(-1+1)^2+6^2}&#10;\\\\\\&#10;d=\sqrt{0+36}\implies d=6

notice, the distance to B is exactly 6, and you know what that means.

\bf ~~~~~~~~~~~~\textit{distance between 2 points}&#10;\\\\&#10;(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad &#10;C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-8})&#10;\\\\\\&#10;\stackrel{distance}{d}=\sqrt{[4-(-1)]^2+[-8-0]^2}\implies d=\sqrt{(4+1)^2+(-8)^2}&#10;\\\\\\&#10;d=\sqrt{25+64}\implies d=\sqrt{89}\implies d\approx 9.43398

notice, C is farther than the radius 6, meaning is outside the circle, hiking about on the plane.
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Read 2 more answers
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