Question

1. cynthia plans to build a tree house that is $\frac{1}{3}$ the size of andrews tree house. cynthia plans to make the area of her tree house at least 13 square feet.

part a
write and solve an inequality to find the area of andrews tree house. let $x$ be the area of andrews tree house.
part b
describe how you know which tree house is larger without solving the inequality.

Explanation:

Step1: Define inequality

Let $x$ = Andrew's tree house area. Cynthia's area is $\frac{1}{3}x$, which is at least 13.
$\frac{1}{3}x \geq 13$

Step2: Solve for $x$

Multiply both sides by 3.
$x \geq 13 \times 3$
$x \geq 39$

For Part B: Cynthia's tree house is explicitly stated to be $\frac{1}{3}$ the size of Andrew's. A fraction less than 1 of a quantity means the original quantity (Andrew's tree house) is larger, since scaling a number by $\frac{1}{3}$ reduces its size.

Answer:

Part A: The inequality is $\frac{1}{3}x \geq 13$, and Andrew's tree house area is at least 39 square feet.
Part B: Andrew's tree house is larger because Cynthia's is only $\frac{1}{3}$ of its size, a fraction less than 1 means the original is bigger.