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?
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
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?
\(a+b+c=99 \)
\(a+6=b-6\\ 5c=b-6\\ c=\frac{b-6}{5}\)
\(a+b+\frac{b-6}{5}=99\\ a-b=-12\\ 2b+ \frac{b-6}{5}=111\\ 10b+b-6=561\\ 11b=549\)
\(b=51\)
\(a+6=b-6\\ a+6=51-6\)
\(a=39\)
\(5c=b-6\\ 5c=51-6\)
\(c=9\)
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