word problems

Question

two of the top grossing concert tours were by a jazz band and a rock band.  Together the two tours visited 169 cities.  The jazz band visted 91 cities more than the rock band.  how many cities did the jazz band visit? how many did the rock band visit?

Answer 1

Let x be the number of cities visited by the jazz band, and let y be the number of cities visited by the rock band. We must solve the following system:

x + y = 169 

x = y + 91.

 

Since the second equation is already solved for x, we can substitute y+91 for x in the first equation giving us y + 91 + y = 169.

Combining like terms, we have 2y + 91 = 169.

Subtracting 91 from both sides gives 2y = 78.

Finally, dividing both sides by 2 gives y = 39, so x = y + 91 = 39 + 91 = 130.

 

Thus the jazz band visited 130 cities, and the rock band visited 39 cities.