A ridiculous SAT question...

I have no idea why I cannot solve this problem. Its from the SAT; any help would be appreciated. (the first part is just the square root of the quantity (x squared plus t squared), I just dont know how to type that.)

(x^2+t^2)^1/2 = 2t-x

If x and t are positive numbers that satisfy the equation above, what is the value of x/t?

[Patrick del Poker Grande]

x^2 + t^2 = 4t^2 - 2tx + x^2
3t^2 = 2tx
3t = 2x

x/t = 3/2

[ QUOTE ]
x^2 + t^2 = 4t^2 - 4 tx + x^2
3t^2 = 4 tx
3t = 4 x

x/t = 3/ 4

[/ QUOTE ]

[Patrick del Poker Grande]

Oops! Nice catch. Sorry for the typo. The idea's right, though.

Thats exactly what I thought, but the book says the answer is 5/4. Whats up?

[Jim T]

[ QUOTE ]
Thats exactly what I thought, but the book says the answer is 5/4. Whats up?

[/ QUOTE ]

Typo.

[pokerdirty]

i haven't done this math in 6 years and i got it correct!!!

gold star please [img]/images/graemlins/smile.gif[/img]

[pzhon]

As with many similar problems, when you have computed the answer, you can check your answer by plugging it back into the original equation.

(4^2+3^2)^(1/2) = 2*4-3.

This is a good habit for more than tests, but it works exceptionally well on the SAT.

[BruceZ]

[ QUOTE ]
I have no idea why I cannot solve this problem. Its from the SAT; any help would be appreciated. (the first part is just the square root of the quantity (x squared plus t squared), I just dont know how to type that.)

(x^2+t^2)^1/2 = 2t-x

If x and t are positive numbers that satisfy the equation above, what is the value of x/t?

[/ QUOTE ]

(x, t, 2t-x) must be a pythagorean triple, meaning that x^2 + y^2 = (2t-x)^2. The first triple (3,4,5) fits the bill, so x = 3, t = 4, and x/t = 3/4. The proof of uniqueness is that this is a SAT question. [img]/images/graemlins/smile.gif[/img]

You can write square root as sqrt(x).