The sum of three numbers is 6. Thrice the thi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the three numbers be $x, y,$ and $z$. According to the problem,we have the following system of linear equations: $x + y + z = 6$  $(1)$ $x + 3

Vedclass · Accepted Answer

$\frac{20}{3}$

Vedclass · Answer

(C) Let the three numbers be $x, y,$ and $z$. According to the problem,we have the following system of linear equations: $x + y + z = 6$  $(1)$ $x + 3z = 7$  $(2)$ $3x + y + z = 12$  $(3)$ Subtracting equation $(1)$ from equation $(3)$: $(3x + y + z) - (x + y + z) = 12 - 6$ $2x = 6 \Rightarrow x = 3$ Substitute $x = 3$ into equation $(2)$: $3 + 3z = 7$ $3z = 4 \Rightarrow z = \frac{4}{3}$ Substitute $x = 3$ and $z = \frac{4}{3}$ into equation $(1)$: $3 + y + \frac{4}{3} = 6$ $y = 6 - 3 - \frac{4}{3} = 3 - \frac{4}{3} = \frac{9-4}{3} = \frac{5}{3}$ The product of the numbers is $xyz = (3) 	imes (\frac{5}{3}) 	imes (\frac{4}{3}) = \frac{20}{3}$.

The sum of three numbers is $6$. Thrice the third number when added to the first number gives $7$. On adding three times the first number to the sum of the second and third numbers,we get $12$. The product of these numbers is:

Similar Questions

For the system of linear equations $x+y+z=6$; $\alpha x+\beta y+7z=3$; $x+2y+3z=14$,which of the following is $NOT$ true?

If ${a_1}x + {b_1}y + {c_1}z = 0, {a_2}x + {b_2}y + {c_2}z = 0, {a_3}x + {b_3}y + {c_3}z = 0$ and $\left| \begin{matrix} {a_1} & {b_1} & {c_1} \\ {a_2} & {b_2} & {c_2} \\ {a_3} & {b_3} & {c_3} \end{matrix} \right| = 0$,then the given system has

If the system of equations
$2x + y - z = 5$
$2x - 5y + \lambda z = \mu$
$x + 2y - 5z = 7$
has infinitely many solutions,then $(\lambda + \mu)^2 + (\lambda - \mu)^2$ is equal to

If $x=\alpha, y=\beta, z=\gamma$ is the solution for the system of equations:
$\begin{aligned} 2x-y+8z &= 13 \\ 3x+4y+5z &= 18 \\ 5x-2y+7z &= 20 \end{aligned}$
then $\alpha\beta+\beta\gamma+\gamma\alpha=$

The number of solutions of the equations $x + 4y - z = 0,$ $3x - 4y - z = 0,$ and $x - 3y + z = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module