Given that the sum of two numbers is 40. The larger number is 10 more than twice the smaller number.
Let x denote the larger number.
Let y denote the smaller number.
The expressions can be written as,
[tex]x+y=40[/tex] ---------(1)
[tex]x=10+2y[/tex] ----------(2)
We need to determine the numbers.
Value of the numbers:
Solving the two equations using the substitution method.
Substitute [tex]x=10+2y[/tex] in equation (1), we have;
[tex]10+2y+y=40[/tex]
[tex]10+3y=40[/tex]
[tex]3y=30[/tex]
[tex]y=10[/tex]
Thus, the value of y is 10.
Substitute [tex]y=10[/tex] in equation (2), we have;
[tex]x=10+2(10)[/tex]
[tex]x=10+20[/tex]
[tex]x=30[/tex]
Thus, the value of x is 30.
Thus, the two numbers are 30 and 10.
