Question

Solve
$15x=10y=6z$
$7x+9y+9z=344$

• A. $x=7,y=12,z=20$
• B. $x=8,y=12,z=20$
• C. $x=8,y=12,z=10$
• D. $x=8,y=9,z=20$

Answer 1

The correct option is B $x=8,y=12,z=20$

We have,
$15x=10y=6z$............(1)
$7x+9y+9z=344$.............(2)

From equation (1) we have,
$15x=10y$

$\Rightarrow y=\frac{3}{2}x$............(3)

Also, $15x=6z$

$\Rightarrow z=\frac{5}{2}x$..........(4)

Substituting equation (3) and equation (4) in the equation (2), we get

$7x+9\left(\frac{3}{2}x\right)+9\left(\frac{5}{2}x\right)=344$

$\Rightarrow \frac{14x+27x+45x}{2}=344$

$\Rightarrow \frac{86x}{2}=344$

$\Rightarrow x=8..........\left(5\right)$

Substituting equation (5) in equation (3), we get

$y=\frac{3}{2}\left(8\right)$

$\Rightarrow y=12$

Substituting equation (5) in equation (4), we get

$z=\frac{5}{2}\left(8\right)$

$\Rightarrow z=20$

Thus, we have $x=8,y=12,z=20$