Answer to Question #43679 in Abstract Algebra for jasleymejia

Question

The two most common names for streets in the United States are Second Street and Main Street, with 15,684 streets bearing one of these names. There are 260 more streets named Second Street than Main Street. (Source: 2006 Tele Atlas digital map data) How many streets bear each name?

Answer 1

Let x is the number of streets that bear name Second Street and y is the number of streets with name Main Street. Then we have the system of equations
x+y=15684
x=y+260
Substitute second equation into the first one and we get
y+260+y=15684
2y=15624
y=7812
and x=7812+260=8072
Answer: 8072 streets with name Second street, 7812 streets with name Main street.