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# algebra

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

Aug 26, 2021

#1
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The value of b is 44/7.

Aug 26, 2021
#2
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a + b + c ==99.......................(1)

[a+5] = [a-5] = [c*5].............(2), solve for a, b, c

Use substitution to get:

a==40,  b==50,   c==9

Aug 26, 2021
#3
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a + b + c = 99

a + 5 = b - 5 ===> a = b + 10

b - 5 = 5c  ===> c = $${b - 5} \over 5$$

so b + 10 + b + $${b - 5} \over 5$$ = 99

so 5b + 50 + 5b + b - 5 = 495

so 11b - 45 = 495

so 11b = 540

so b = $$540 \over 11$$

Aug 26, 2021
#4
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wait, made a mistake, a = b - 10

so

5b - 50 + 5b + b - 5 = 495

11b - 55 = 495

11b = 550

so b = 50

Guest Aug 26, 2021
#5
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