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saul85 [17]
3 years ago
15

At a regional soccer​ tournament, tickets for two adults and seven students cost ​$60. Tickets for three adults and eleven stude

nts cost ​$93. Determine the price of an adult ticket and the price of a student ticket.
The price of an adult ticket is ​$, and the price of a student ticket is ​$
Mathematics
1 answer:
den301095 [7]3 years ago
8 0

Answer:

The price of an adult ticket is $9 and the price of a student ticket is $6

Step-by-step explanation:

Create a system of equations where x is the price of an adult ticket and y is the price of a student ticket:

2x + 7y = 60

3x + 11y = 93

Solve by elimination by multiplying the top equation by 3 and the bottom equation by -2, to cancel out the x terms:

6x + 21y = 180

-6x - 22y = -186

Add them together:

-y = -6

y = 6

Then, plug in 6 as y into one of the equations to solve for x:

2x + 7y = 60

2x + 7(6) = 60

2x + 42 = 60

2x = 18

x = 9

So, the price of an adult ticket is $9 and the price of a student ticket is $6

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For each customer, there are only two possible outcomes, either they receive the coupon, or they do not. The probability of a customer receiving the coupon is independent of any other customer, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

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In this problem:

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The probability that <u>neither receives a coupon is P(X = 0)</u>, thus:

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P(X = 0) = C_{2,0}.(0.1)^{0}.(0.9)^{2} = 0.81

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A similar problem is given at brainly.com/question/25326823

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