Question

(8/m +12/n =1/10) and (1/14 =6/m +8/n) Then solve for m and n.

Answer 1

Answer:

m =140

n = 280

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Step-by-step explanation:

8/m + 12/n = 1/10

6/m + 8/n = 1/14

Let say m = 1/x   & n = 1/y

8x + 12y = 1/10    EqA

6x + 8y = 1/14     EqB

2*EqA - 3*EqB

16x + 24y - 18x - 24 y = 1/5 - 3/14

-2x = (1/70)(14-15)

-2x = -1/70

x = 1/140

putting vale of x in EqA

8/140 +12y = 1/10

8 + 12*140 y = 14

y = 6/(12*140)

y = 1/280

m = 1/x = 140

n = 1/y = 280

Answer 2

Answer:

Value of m is 140 and the value of n is 280.

Step-by-step explanation:

$Given\:equations: \dfrac{8}{m} +\dfrac{12}{n}=\dfrac{1}{10}\quad\quad \it{...(i)}$

$2. \quad \quad \quad \:\:\;\dfrac{6}{m}+\dfrac{8}{n}=\dfrac{1}{14}\quad\quad\it{...(ii)}$

Now, in equation ( i ),

$\implies \dfrac{8}{m} +\dfrac{12}{n}=\dfrac{1}{10}\\\\\\\implies \dfrac{8n+12m}{mn}=\dfrac{1}{10}\\\\\\\implies \dfrac{mn}{8n+12m}=10\\\\\\\implies mn = 10(8n+12m)\\\\\\\implies mn = 80n + 120m\quad\quad\it{...( iii )}$

Then, in equation ( ii ),

$\implies \dfrac{6}{m}+\dfrac{8}{n}=\dfrac{1}{14}\\\\\\\implies \dfrac{6n +8m}{mn}=\dfrac{1}{14}\\\\\\\implies \dfrac{mn}{6n+8m}=14\\\\\\\implies mn=14(6n + 8m )\\\\\\\implies mn = 84n+ 112m\quad\quad\it{...( iv )}$

Comparing ( iii ) and ( iv ),

= >  mn = mn

= > 80n + 120m = 84n + 112m

= > 4( 20n + 30m ) = 4( 21n + 28m )

= > 20n + 30m = 21n + 28m

= > 30m - 28m = 21n - 20n

= > 2m = n            ...( v )

Substituting the value of n in ( i ),

= >  8 / m + 12 / n = 1 / 10

= >  8 / m  + 12 / 2m = 1 / 10

= > 8 / m + 6 / m = 1 / 10

= > ( 8 + 6 ) / m = 1 / 10

= >  14 / m = 1 / 10

= > 14 x 10 = m

= >  140 = m

Hence,

= >  2m = n

= >  2 x 140 = n

= >  280 = n

Therefore the value of m is 140 and the value of n is 280.