John R. answered • 06/08/13
John R: Math, Science, and History Teacher
The first step we need to take is to write an equation that represents the number of auto collisions that occur each year. Since the baseline year (1998) involved 26 collisions, 26 will be the constant. Since the decrease is 2.5 per year, the coefficient on the variable (the slope) will be -2.5.
I am going to use y to represent number of collisions and x to represent the number of years since 1998.
y = -2.5x + 26
Since we want to know how many years it will take until there are only 10 collisions, we are going to use 10 for y and solve for x.
y = - 2.5x + 26 Equation derived from story problem.
10 = -2.5x + 26 Substitute 10 for y
10 - 26 = -2.5x Subtract 26 from each side
-16 = -2.5x Simplify
-16/(-2.5) = x Divide each side by -2.5
6.4 = x Simplify
x = 6.4 Symmetric property
You will probably want to round up to 7 years, because the accidents are going to be counted for calendar years, and rounding down to 6 years will still leave more than 10 accidents.
