How do I algebraically solve this problem?
200/(r+10) = 200/r -1
I know the answer is obviously 40 from looking at it but how do i manipulate this equation to give me this?
200/(r+10) = 200/r -1
I know the answer is obviously 40 from looking at it but how do i manipulate this equation to give me this?
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200 / (r + 10) = 200 / r − 1
Multiply by (r + 10) on both sides:
200 = (200 / r − 1)(r + 10)
Multiply by r on both sides:
200r = (200 − r)(r + 10)
Multiply out:
200r = − r^2 + 190r + 2000
Rearrange to standard quadratic form:
r^2 + 10r − 2000 = 0
Factor:
(r − 40)(r + 50) = 0
Solutions:
[r = 40] or [r = − 50]
Multiply by (r + 10) on both sides:
200 = (200 / r − 1)(r + 10)
Multiply by r on both sides:
200r = (200 − r)(r + 10)
Multiply out:
200r = − r^2 + 190r + 2000
Rearrange to standard quadratic form:
r^2 + 10r − 2000 = 0
Factor:
(r − 40)(r + 50) = 0
Solutions:
[r = 40] or [r = − 50]