Question

heather and joe are growing sunflowers in their backyards. heather’s sunflowers are currently 36 inches tall and grow 6 inches monthly. joe’s sunflowers are only 24 inches tall but grow 9 inches monthly. after how many months will joe’s sunflowers be taller than heather’s? let x represent the number of months heather and joe grow their sunflowers. drag and drop the correct answer in each box. the inequality that represents the situation is \boxed{} + 9x \boxed{} \boxed{} + \boxed{} joe’s sunflowers will be taller than heather’s after \boxed{} months.

Explanation:

Step1: Define height expressions

Heather's height: $36 + 6x$; Joe's height: $24 + 9x$

Step2: Set up inequality for taller height

We want Joe's height > Heather's height:
$24 + 9x > 36 + 6x$

Step3: Simplify the inequality

Subtract $6x$ from both sides:
$24 + 3x > 36$
Subtract 24 from both sides:
$3x > 12$
Divide by 3:
$x > 4$

Answer:

The inequality that represents the situation is $\boldsymbol{24 + 9x > 36 + 6x}$
Joe's sunflowers will be taller than Heather's after $\boldsymbol{4}$ months.