Question

In this activity, you will use a variable to create expressions for various relationships. Then you will use these expressions to form a linear equation. Finally, you will find the solution to the equation.

Theresa has two brothers, Paul and Steve, who are both the same height. Paul says he is inches shorter than twice Theresa’s height. Steve says he is inches shorter than three times Theresa’s height. If they are both right, how tall is Theresa?

a. T−2 inches
b. 2T−1 inches
c. 3T−1 inches
d. 2T+1 inches

Answer 1

To find Theresa's height, we express her brothers' heights in terms of Theresa's height, create an equation, and solve for Theresa's height once the specific inch differences are known.

Step-by-step explanation:

Let's denote Theresa's height as T inches. Since Paul is inches shorter than twice Theresa's height, we can express his height as 2T - n inches, where n is the number of inches shorter than twice Theresa's height. Similarly, since Steve is inches shorter than three times Theresa's height, we can express his height as 3T - m inches, where m is the number of inches shorter than three times Theresa's height.

Given that Paul and Steve are the same height, we then set the two expressions equal to each other to form an equation: 2T - n = 3T - m. This equation can be solved to find the value of T once the values of n and m are known, determining Theresa's height.