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:
[tex] x + y = 65[/tex]
2. One number is 4 times and large as the other:
[tex] x=4y [/tex]
We can then solve by substitution:
[tex]x+y=65[/tex]
[tex]4y+y=65[/tex]
[tex]5y=65[/tex]
[tex]\frac{5y}{5}=\frac{65}{5}[/tex]
[tex]y=13[/tex]
[tex]x=4y[/tex]
[tex]x=4(13)=52[/tex]
The numbers are 13 and 52.
