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

Answer:

The numbers 'x' and 'y' are:

$x=56,\:y=36$

Step-by-step 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

$\frac{1}{8}x\:+\:\frac{1}{3}y=19$

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

$\begin{bmatrix}\frac{1}{8}x+\frac{1}{3}y=19\\ x+y=92\end{bmatrix}$

$\mathrm{Multiply\:}\frac{1}{8}x+\frac{1}{3}y=19\mathrm{\:by\:}8\:\mathrm{:}\:\quad \:x+\frac{8}{3}y=152$

$\begin{bmatrix}x+\frac{8}{3}y=152\\ x+y=92\end{bmatrix}$

$x+y=92$

$-$

$\underline{x+\frac{8}{3}y=152}$

$-\frac{5}{3}y=-60$

$\begin{bmatrix}x+\frac{8}{3}y=152\\ -\frac{5}{3}y=-60\end{bmatrix}$

solve for y

$-\frac{5}{3}y=-60$

$-5y=-180$

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

$\frac{-5y}{-5}=\frac{-180}{-5}$

$y=36$

$\mathrm{For\:}x+\frac{8}{3}y=152\mathrm{\:plug\:in\:}y=36$

$x+\frac{8}{3}\cdot \:36=152$

$x=56$

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

$x=56,\:y=36$