In a contest, each finalist must answer 5 questions correctly. Each question is worth twice as much as the question before it. The fifth question is worth $1,600. How much is the first question worth?
Let X be the value of the first question.
The second question is worth 2*X.
The third question is worth 2*2*X=4*X.
The fourth question is worth 2*4*X=8*X.
The total value of answering all questions is X+2*X+4*X+8*X+1600=15*X+1600.
The total value is $4,000.
15*X+1600=$4000
15*X=$4000-1600=2400
15*X=2400
X=2400/15
X=$<<160>>160. Answer: \boxed{160}.
To find the value of the first question, we need to work backwards from the value of the fifth question.
Let's call the value of the first question x.
The second question is worth twice as much as the first question, so its value is 2x.
The third question is worth twice as much as the second question, so its value is 2 * 2x = 4x.
The fourth question is worth twice as much as the third question, so its value is 2 * 4x = 8x.
Finally, the fifth question is worth $1,600, so its value is 8x = $1,600.
To find x, we can divide both sides of the equation by 8:
8x / 8 = $1,600 / 8
x = $200
Therefore, the first question is worth $200.
To find the value of the first question, we can work backwards from the value of the last question.
We are given that the fifth question is worth $1,600.
Let's call the value of the first question "x".
The second question is worth twice as much as the first, so its value is 2x.
The third question is worth twice as much as the second, so its value is 2(2x) = 4x.
The fourth question is worth twice as much as the third, so its value is 2(4x) = 8x.
Finally, the fifth question is worth $1,600, so its value is 8x = $1,600.
To find the value of x, we can divide both sides of the equation by 8:
8x/8 = $1,600/8
x = $200
Therefore, the first question is worth $200.