Question

The sum of two numbers is 92. One eighth of the larger number plus one third of the smaller number is 19. Find the numbers.​

Answer 1

The numbers 'x' and 'y' are:

`x=56,\:y=36`

Explanation:

Let 'x' and 'y' be the two numbers

As the sum of the two numbers is 92.

so

`x+y = 92`

Given that One-eighth of the larger number plus one-third of the smaller number is 19.

so

`(1)/(8)x\:+\:(1)/(3)y=19`

now solving both equations to determine the numbers 'x' and 'y'.

`\begin{bmatrix}(1)/(8)x+(1)/(3)y=19\\ x+y=92\end{bmatrix}`

`\mathrm{Multiply\:}(1)/(8)x+(1)/(3)y=19\mathrm{\:by\:}8\:\mathrm{:}\:\quad \:x+(8)/(3)y=152`

`\begin{bmatrix}x+(8)/(3)y=152\\ x+y=92\end{bmatrix}`

`x+y=92`

`-`

`\underline{x+(8)/(3)y=152}`

`-(5)/(3)y=-60`

`\begin{bmatrix}x+(8)/(3)y=152\\ -(5)/(3)y=-60\end{bmatrix}`

solve for y

`-(5)/(3)y=-60`

`-5y=-180`

`\mathrm{Divide\:both\:sides\:by\:}-5`

`(-5y)/(-5)=(-180)/(-5)`

`y=36`

`\mathrm{For\:}x+(8)/(3)y=152\mathrm{\:plug\:in\:}y=36`

`x+(8)/(3)\cdot \:36=152`

`x=56`

Thus, the numbers 'x' and 'y' are:

`x=56,\:y=36`