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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 ?​

Respuesta :

Answer:

Theresa's height is 60 inches

Step-by-step explanation:

The given parameters are;

The height of Paul = The height of Steve

Paul's height = [tex]1\dfrac{1}{2}[/tex] times Theresa's height - 16 inches

Steve's height = [tex]1\dfrac{1}{3}[/tex] times Theresa's height - 6 inches

Let 'T' represents Theresa's height, we have;

Paul's height = [tex]1\dfrac{1}{2}[/tex] ×T - 16

Steve's height = [tex]1\dfrac{1}{3}[/tex] ×T - 6

Paul's height = Steve's height

Therefore;

[tex]1\dfrac{1}{2}[/tex] ×T - 16 = [tex]1\dfrac{1}{3}[/tex] ×T - 6

[tex]1\dfrac{1}{2}[/tex] ×T - [tex]1\dfrac{1}{3}[/tex] ×T = 10

[tex]#\dfrac{3}{2}[/tex] ×T - [tex]\dfrac{4}{3}[/tex] ×T = 10

[tex]\dfrac{1}{6}[/tex] ×T = 10

T = 10 × 6 = 60

Theresa's height, T = 60 inches

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