the diagram part of holly's design for a game. In her game a player pays x pence to spin a star. when the star stops spinning the payer wins the amount shown on the arrow. holly wants to gain an average of 5p each time the game is played show how this can be done by adding six more numbers to the star and finding a suitable value for x

Students' numbers on star

(average of numbers on star = x-5)
For example, if it costs 15p to play the game, x =15. Average win should be x-5=10p. Therefore numbers add up to 10*6= 60

the answer above is wrong

there is part to the question that is missing ad it's a diagram of holly's spinner and since i cannot upload the picture the answer won't make much sense.

so the answer goes somewhere along the lines of:

(x-10)+(x-2)+((x-something)x6)/8

which gives:
(x-10)+(x-2)+((x-something)x6)= 40
8x-12-(the something called a)=40
8x-a=40
x-a/8= 5

and this is where it stops because i cannot solve an equation with two unknown values. so its all about finding that a and then finding x. i personally think that its to do with trial and error but i'm not too sure. i hope i helped and i'm sorry if you didn't understand this but this is all i can do considering that there is a missing part to this problem.

there are some spelling mistakes in the answer above! sorry! e.g:'ad' is actually 'and'

To help Holly gain an average of 5p each time the game is played, we can add six more numbers to the star and determine a suitable value for x.

Let's start by analyzing the given information. Currently, there is no specific information about the numbers on the star or the probabilities of winning various amounts. Therefore, we can assign arbitrary values to the initial numbers on the star.

To ensure that Holly gains an average of 5p each time the game is played, we can consider the expected value of the outcomes. The expected value is the sum of each outcome multiplied by its probability.

Let's assume the initial numbers on the star are 1p, 2p, and 3p, with equal probabilities of 1/3 each. Since we need to gain an average of 5p, we can add six more numbers with specific probabilities to achieve this.

For simplicity, let's add two more numbers of 4p, two numbers of 6p, and two numbers of 8p. To maintain equal probability for each number, we will allocate 1/12 probability to each of these new numbers. This results in a total of 12 numbers on the star.

To determine a suitable value for x, we need to calculate the expected value based on the new distribution of numbers and probabilities.

Expected value (E) = (1p * 1/12) + (2p * 1/12) + (3p * 1/12) + (4p * 1/12) + (4p * 1/12) + (6p * 1/12) + (6p * 1/12) + (8p * 1/12) + (8p * 1/12)

E = (1/12) * (1 + 2 + 3 + 4 + 4 + 6 + 6 + 8 + 8) = (1/12) * 42 = 3.5p

As we can observe, the expected value obtained using this arrangement is 3.5p, not 5p. To achieve an average gain of 5p, we need to increase the value of x.

To find the suitable value for x, we can use the following formula:

E = (x * P) + (4p * 1/12) + (4p * 1/12) + (6p * 1/12) + (6p * 1/12) + (8p * 1/12) + (8p * 1/12)

Substituting E = 5p, which is our desired average gain, we can solve for x:

5 = (x * P) + (4p * 1/12) + (4p * 1/12) + (6p * 1/12) + (6p * 1/12) + (8p * 1/12) + (8p * 1/12)

Simplified further:

5 = (x * P) + 2/12 * (4p + 4p + 6p + 6p + 8p + 8p)
5 = (x * P) + 2/12 * 36p

To isolate x, we'll need to solve the equation for P:

P + 2/12 * 3p = 5

Simplifying further:

P + 1/2 * p = 5
P + 0.5p = 5

Now, we can determine the value of P:

1.5p = 5
p = 5 / 1.5
p = 3.33

Therefore, a suitable value for x, which would result in an average gain of 5p for Holly's game, is 3.33 pence.