Question

Jerry planted a pine tree that was 5 feet tall and a maple tree that was 10 feet tall. The pine tree grew 3 feet taller per year and the maple tree grew 2 feet taller per year. Which comparison is described by the inequality below? After x years, the pine tree is taller than the maple tree. After x years, the pine tree is at least as tall as the maple tree. After 3x years, the pine tree is taller than the maple tree was after 2x years. After 3x years, the pine tree is at least as tall as the maple tree was after 2x years.

Answer 1

The initial length of the pine tree=5 feet.

Groth rate of pine tree =3 feet/year.

The initial length of the pine tree =10 feet.

Groth rate of the maple tree =2 feet/year.

After x years, the height of the pine tree= 5+3x feet and

after x years, the height of the maple tree= 10+2x feet.

The inequality for which, after x year, the pine tree is taller than the maple tree is

$5+3x>10+2x$

$\Rightarrow x>5$ .

The inequality for which, the pine tree is at least as tall as the maple tree is $5+3x\geq10+2x$.

$\Rightarrow x\geq 5$ .

Again, after 3x years, the height of the pine tree= 5+3(3x)=5+9x feet and

after 2x years, the height of the maple tree= 10+2(2x)=10+4x feet.

The inequality for which, after 3x years, the pine tree is taller than the maple tree was after 2x years is

$5+9x>10+4x$

$\Rightarrow 5x>5$

$\Rightarrow x>1.$

The inequality for which, the pine tree is at least as tall as the maple tree is $5+9x\geq10+4x$.

$\Rightarrow 5x\geq5$

$\Rightarrow x\geq 1.$