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l=(125 )/(m)+50 n
The equation gives the quantity 
l in terms of the quantities 
m and 
n. Which of the following equations correctly expresses 
n in terms of 
l and 
m ?
Choose 1 answer:
(A) 
n=(l-125)/(50 m)
(B) 
n=(l)/( 50)-(125 )/(m)
(C) 
n=(l)/( 50)-(5)/(2m)
(D) 
n=(5)/(2m)-(l)/( 50)

l=125m+50n l=\frac{125}{m}+50 n \newlineThe equation gives the quantity l l in terms of the quantities m m and n n . Which of the following equations correctly expresses n n in terms of l l and m m ?\newlineChoose 11 answer:\newline(A) n=l12550m n=\frac{l-125}{50 m} \newline(B) n=l50125m n=\frac{l}{50}-\frac{125}{m} \newline(C) n=l5052m n=\frac{l}{50}-\frac{5}{2 m} \newline(D) n=52ml50 n=\frac{5}{2 m}-\frac{l}{50}

Full solution

Q. l=125m+50n l=\frac{125}{m}+50 n \newlineThe equation gives the quantity l l in terms of the quantities m m and n n . Which of the following equations correctly expresses n n in terms of l l and m m ?\newlineChoose 11 answer:\newline(A) n=l12550m n=\frac{l-125}{50 m} \newline(B) n=l50125m n=\frac{l}{50}-\frac{125}{m} \newline(C) n=l5052m n=\frac{l}{50}-\frac{5}{2 m} \newline(D) n=52ml50 n=\frac{5}{2 m}-\frac{l}{50}
  1. Given equation: We start with the given equation:\newlinel=125m+50n l = \frac{125}{m} + 50n \newlineOur goal is to solve for n n in terms of l l and m m .
  2. Isolating the term containing nn: First, we isolate the term containing nn on one side of the equation by subtracting 125m\frac{125}{m} from both sides:\newlinel125m=50nl - \frac{125}{m} = 50n
  3. Dividing both sides by 5050: Next, we divide both sides of the equation by 5050 to solve for nn:n=(l125m)50n = \frac{\left(l - \frac{125}{m}\right)}{50}
  4. Simplifying the right side: Now, we simplify the right side of the equation by distributing the division by 5050 to both terms in the numerator:\newlinen=(l50)(125m50)n = \left(\frac{l}{50}\right) - \left(\frac{\frac{125}{m}}{50}\right)
  5. Further simplification: We simplify the second term by dividing 125125 by 5050: \newlinen=(l50)(12550m)n = \left(\frac{l}{50}\right) - \left(\frac{125}{50m}\right)
  6. Expressing 2.52.5 as a fraction: We further simplify the second term by reducing the fraction 12550\frac{125}{50}, which simplifies to 2.52.5: \newlinen=(l50)(2.5m)n = (\frac{l}{50}) - (\frac{2.5}{m})
  7. Expressing 22.55 as a fraction: We further simplify the second term by reducing the fraction 12550\frac{125}{50}, which simplifies to 2.52.5:\newlinen=(l50)(2.5m)n = (\frac{l}{50}) - (\frac{2.5}{m})Finally, we express 2.52.5 as a fraction in terms of 22 to match the answer choices:\newline2.52.5 is the same as 52\frac{5}{2}, so we rewrite the equation as:\newlinen=(l50)(52m)n = (\frac{l}{50}) - (\frac{5}{2m})

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