City A's population of 1115000 is decreasing at a rate of 15000 per year. City B's population of 698000 is increasing at a rate of 45000 per year. In how many years will the populations be equal? Form the equation and round the answer to the nearest whole number.

7 years

Step-by-step explanation:

Let x be number of years the populations be equal

City A's population of 1115000 is decreasing at a rate of 15000 per year.

The population is decreasing at a constant rate so we use equation

y = mx + b

where m is the slope (rate), b is the initial population

m = - 15000 (decreasing), b = 1115000

y = - 15000 x + 1115000

City B's population of 698000 is increasing at a rate of 45000 per year.

m = 45000 (increasing), b = 698000

y = 45000 x + 698000

Now we set the equations equal and solve for x

45000 x + 698000 = - 15000 x + 1115000

Add 15000 on both sides

60000 x + 698000 = 1115000

Subtract 689000 on both sides

60000 x = 417000

Divide by 60000 on both sides

x = 6.95

So after 7 years the population will be equal.