In a television game show, there are five questions to answer. Each question is worth twice as much as the previous question. If the last question was worth $6400, what was the first question worth?
is the answer 400
Yes.
Working backwards:
5 - 6400
4 - 3200
3 - 1600
2 - 800
1 - 400
To find the value of the first question, we need to determine the pattern in the values of the questions. We know that each question is worth twice as much as the previous one.
Let's denote the value of the first question as x.
The second question would be worth 2 times the value of the first question, which is 2x.
The third question would be worth 2 times the value of the second question, which is 2(2x) = 4x.
The fourth question would be worth 2 times the value of the third question, which is 2(4x) = 8x.
The fifth question would be worth 2 times the value of the fourth question, which is 2(8x) = 16x.
We are given that the value of the fifth question is $6400. So, we can set up the equation:
16x = 6400
To find the value of x, we divide both sides of the equation by 16:
x = 6400/16
Simplifying:
x = 400
Therefore, the value of the first question is $400.