Answer:
[tex]x=36[/tex]
[tex]y=6[/tex]
Step-by-step explanation:
Let x be the large number and y be the small number.
Given:
The sum of two numbers is 40.
So the first relation is.
[tex]x+y=40[/tex]---------(1)
The large value is divided by smaller value.
So, [tex]\frac{x}{y} [/tex], and the quotient is 5 and the remainder is 4.
and second relation is.
[tex]\frac{x}{y} =5+\frac{4}{y}[/tex]
[tex]\frac{x}{y} =\frac{5y+4}{y}[/tex]
The denominator y is cancelled both side.
[tex]x = 5y + 4[/tex]
x value put in the equation 1
[tex]5y+4+y=40[/tex]
[tex]6y=40-4\\y=\frac{36}{6} \\y=6[/tex]
Put y value in equation 1
[tex]x+6=40[/tex]
[tex]x=40-6[/tex]
[tex]x=36[/tex]
Therefore, x value is 36 and y value is 6.
