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 times Theresa’s height. Steve says he is inches shorter than times Theresa’s height. If they are both right, how tall is Theresa? To solve a problem like this one, you can use a linear equation where the variable represents Theresa’s height in inches. Let represent Theresa’s height in inches. Question 1 The relationships for Paul’s and Steve’s height with respect to Theresa’s height are described above. First you will write expressions for Paul’s height and for Steve’s height. Then you will relate the expressions. Part B Write an expression to represent Steve’s height in inches.

Step-by-step explanation:

Some information is missing. The correct question is:

Theresa has two brothers, Paul and Steve, who are both the same height. Paul says he is 16 inches shorter than 1 1/2 times Theresa's height. Steve says he's 6 inches shorter than 1 1/3 times Theresa's height. If they're both right, how tall is Theresa?

Solution:

Let p represent Paul's height

Let s represent Steve's height

Let t represent Theresa's height

Since Paul and Steve are both of the same height, it means that p = s

Paul says he is 16 inches shorter than 1 1/2 times Theresa's height. It means that

p = 1.5t - 16

Steve says he's 6 inches shorter than 1 1/3 times Theresa's height. It means that

s = 4t/3 - 6

Since p = s, then

p = 4t/3 - 6

Therefore, it means that

1.5t - 16 = 4t/3 - 6

Multiplying through by 3, it becomes

4.5t - 48 = 4t - 18

4.5t - 4t = - 18 + 48

0.5t = 30

t = 30/0.5 = 60 inches

Theresa's height is 60 inches

x = 3 ± √(5+y)