Call the two numbers 'x' and 'y'. We can then set up two equations (using the given information) to represent the relationships between the numbers:
1. The sum of the two numbers is 65:
\(x + y = 65\)
2. One number is 4 times and large as the other:
\(x=4y\)
We can then solve by substitution:
\(x+y=65\)
\(4y+y=65\)
\(5y=65\)
\(\frac{5y}{5}=\frac{65}{5}\)
\(y=13\)
\(x=4y\)
\(x=4(13)=52\)
The numbers are 13 and 52.
