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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 $1600. How much is the first quesiton worth?

Sagot :

2019327
you must divide 1600 by 2 five times to get 1600/2=800, 800/2=400, 400/2=200, 200/2=100, and finally 10/2=50, so the first question is worth $50

Answer:

The first question worth $100

Step-by-step explanation:

Let's call [tex]X_1, X_2, X_3, X_4, X_5[/tex] the worth of the first, second, third, fourth and fifth question respectively.

From the question, we know that each question is worth twice as much as the question before it and the fifth question worth $1600. We can write that as:

[tex]X_2=2X_1\\X_3=2X_2\\X_4=2X_3\\X_5=2X_4\\X_5=1600[/tex]

If we replace the values of [tex]X_2, X_3, X_4[/tex] as following:

[tex]X_3=2X_2=2(2X_1)=4X_1\\X_4=2X_3=2(4X_1)=8X_1\\X_5=2X_4=2(8X_1)=16X_1[/tex]

Then, we can find the value of [tex]X_1[/tex] as:

[tex]X_5=1600\\16X_1=1600\\X_1=\frac{1600}{16} =100[/tex]

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