Question

The solution set of the equation: m/10+n/5=15 ; m/8+n/6=15

Answer 1

Answer

$\sf \dashrightarrow \dfrac{m}{10} + \dfrac{n}{5} = 15 \: \: --- (i)$

$\sf \dashrightarrow \dfrac{m}{8} + \dfrac{n}{6} = 15 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow \dfrac{m}{10} + \dfrac{n}{5} = 15$

$\sf \dashrightarrow \dfrac{m + 2n}{10} = 15$

$\sf \dashrightarrow m + 2n = 15 \times 10$

$\sf \dashrightarrow m + 2n = 150 \: \: --- (iii)$

By second equation,

$\sf \dashrightarrow \dfrac{m}{8} + \dfrac{n}{6} = 15$

$\sf \dashrightarrow \dfrac{3m + 4n}{24} = 15$

$\sf \dashrightarrow 3m + 4n = 15 \times 24$

$\sf \dashrightarrow 3m + 4n = 360 \: \: --- (iv)$

By third equation,

$\sf \dashrightarrow m + 2n = 150$

$\sf \dashrightarrow m = 150 - 2n$

Now, let's find the value of y by fourth equation

$\sf \dashrightarrow 3m + 4n = 360$

$\sf \dashrightarrow 3(150 - 2n) + 4n = 360$

$\sf \dashrightarrow 450 - 6n + 4n = 360$

$\sf \dashrightarrow 450 - 2n = 360$

$\sf \dashrightarrow -2n = 360 - 450$

$\sf \dashrightarrow -2n = -90$

$\sf \dashrightarrow n = \dfrac{-90}{-2}$

$\sf \dashrightarrow n = 45$

Now, we should find the value of x by third equation.

$\sf \dashrightarrow m + 2n = 150$

$\sf \dashrightarrow m + 2(45) = 150$

$\sf \dashrightarrow m + 90 = 150$

$\sf \dashrightarrow m = 150 - 90$

$\sf \dashrightarrow m = 60$

Hence, the values of m and n are 60 and 45 respectively.