Question

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 ?​

Answer 1

Theresa's height is 60 inches

Explanation:

The given parameters are;

The height of Paul = The height of Steve

Paul's height =
`1(1)/(2)` times Theresa's height - 16 inches

Steve's height =
`1(1)/(3)` times Theresa's height - 6 inches

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

Paul's height =
`1(1)/(2)` ×T - 16

Steve's height =
`1(1)/(3)` ×T - 6

Paul's height = Steve's height

Therefore;

`1(1)/(2)` ×T - 16 =
`1(1)/(3)` ×T - 6

`1(1)/(2)` ×T -
`1(1)/(3)` ×T = 10

`#(3)/(2)` ×T -
`(4)/(3)` ×T = 10

`(1)/(6)` ×T = 10

T = 10 × 6 = 60

Theresa's height, T = 60 inches