Question

29] Find the value of two numbers if the first number minus the second number is 154. And 3 timesthe first number plus two times the second number is 358.

Answer 1

Let x be the first number and y be the second number.

Given, the first number minus the second number is 154. Therefore,

`x-y=154\ldots\ldots.(1)`

Given, 3 times the first number plus two times the second number is 358. Therefore,

`3x+2y=358\ldots\ldots.(2)`

Multiply equation (1) by 2.

`2x-2y=308\ldots\ldots.(3)`

Now, add equations (2) and (3) to find x.

`\begin{gathered} 3x+2x+2y-2y=358+308 \\ 5x=666 \\ x=(666)/(5)=133.2 \end{gathered}`

Put x=133.2 in equation (1) to find y.

`\begin{gathered} 133.2-y=154 \\ 133.2-154=y \\ -20.8=y \end{gathered}`

Therefore, the first number x is 133.2 and the second number y is -20.8.

To check the answer, put y=-20.8 and x=133.2 in equation (1) and check if the left hand side of equation equals right hand side of equation.

LHS of equ. (1) is,

`\begin{gathered} x-y \\ 133.2-(-20.8) \\ 133.2+20.8=154 \end{gathered}`

We know, RHS of equ. (1) is 154.

So, LHS=RHS, and hence, the x and y values satisfies the equation.