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The sum of three numbers a, b, and c is 99. If we increase a by 6, decrease b by 6 and multiply c by 5, the three resulting numbers are equal. What is the value of b?

 Oct 4, 2019
 #1
avatar+104962 
+3

a + b + c  = 99

 

And if

a + 6  = b - 6

Then  b = a + 12

 

 

And  a + 6  = 5c   ⇒   [a + 6] / 5  = c  

 

So

 

a + b + c  =  99

 

a  + ( a + 12)  +  [ a  + 6 ] / 5  = 99      multiply through by 5

 

5a + 5a  + 60 +  a + 6  =  495      simplify

 

11a  + 66 = 495       subtract 66 from both sides

 

11a  = 429     divide both sides by 11

 

a  =  39

 

b = a+ 12  =  51

 

 

cool cool cool

 Oct 4, 2019
edited by CPhill  Oct 4, 2019
edited by CPhill  Oct 4, 2019
 #2
avatar+8652 
+2


The sum of three numbers a, b, and c is 99. If we increase a by 6, decrease b by 6 and multiply c by 5, the three resulting numbers are equal. What is the value of b?

 

Die Summe der drei Zahlen a, b und c ist 99. Wenn wir a um 6 erhöhen, b um 6 verringern und c mit 5 multiplizieren, sind die drei resultierenden Zahlen gleich. Was ist der Wert von b?

 

\(a+b+c=99 \)

\(a+6=b-6\\ 5c=b-6\\ c=\frac{b-6}{5}\)

\(a+b+\frac{b-6}{5}=99\\ a-b=-12\\ 2b+ \frac{b-6}{5}=111\\ 10b+b-6=561\\ 11b=549\)
\(b=51\)

\(a+6=b-6\\ a+6=51-6\)

\(a=39\)

\(5c=b-6\\ 5c=51-6\)

\(c=9\)

laugh  !

 Oct 4, 2019
edited by asinus  Oct 4, 2019

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