Question

A rubber tree is 95 inches tall and growing at a rate of 4 inches per year. A cactus is 40 inches tall and growing at arate of 5 inches per year. After how many years will the rubber tree be shorter than the cactus tree

Answer 1

The rubber tree starts off at 95 in and increases 4in per year. We can write this as 95 + 4y (y representing the number of years) the cactus tree starts off at 40 in and increases 5 in per year so we can write is as 40 + 5y. We want to find out y when the cactus is taller so
95+4y < 40+5y And we solve for y
Subtract 40 from both sides
55+4y < 5y
Subtract 4y from both sides
55 < y
Y is any number over 55 but we need the year when the cactus will be taller
So in 56 years the cactus will be taller.