Question

Theresa has two brothers, Paul and Steve, who are both the same height. Paul says he is 16 inches shorter than 1 and a half times Theresa’s height. Steve says he is 6 inches shorter than 1 and one third times Theresa’s height if they are both right how tall is Theresa?

Answer 1

60 inches tall

Explanation:

Answer 2

Theresa is 60 inches tall

Explanation:

Let Theresa's height be t.

Let Paul's height be p.

Let Steve's height be s.

Paul says he is 16 inches shorter than 1 and a half times Theresa’s height. This means that:

p = 3/2 t - 16 = 3t/2 - 16 ________(1)

Steve says he is 6 inches shorter than 1 and one third times Theresa’s height. This means that:

s = 4/3 t - 6 = 4t/3 - 6 __________(2)

Since they are both right and they have the same height, we can equate (1) and (2):

3t/2 - 16 = 4t/3 - 6

Collect like terms:

3t/2 - 4t/3 = 16 - 6 = 10

t/6 = 10

=> t = 6 * 10 = 60 inches

Theresa is 60 inches tall.