Word problems and probability trees help

Question

1. A group of 5 adults and 3 children paid a total of $108 for their concert tickets. Another group of 3 adults and 10 children paid $155. Find the cost of an adult ticket and the cost of a child’s ticket.

2. A vanilla thick shake is $2 more than a fruit juice. If 3 vanilla thick shakes and 5 fruit juices cost $30, determine their individual prices.

3. A caterer makes a variety of sandwiches, 4 salads, 3 hams, and 5 cheeses. The total of 12 sandwiches is on one large plate. A guest takes two sandwiches at random from the plate no one else has touched yet.

Salad (S). Ham (H). Cheese (C). Total of 12, 4 salad, 3 ham & 5 cheese.

(a) Draw a tree diagram to show all possible outcomes.

(b) How many outcomes are there?

(c) What is the probability that both sandwiches are salad? Pr(C,C)

(d) What is the probability of selecting at least one salad sandwich?

Hints: once a sandwich is selected from a total of 12 then the next pick will be out of 11.

4. A sports shop obtains shoes from two suppliers, supplier A and B. It is known that 5% (0.05) of the shoes from supplier A are defective, where 9% (0.09) are defective from supplier B.

The shop owner obtains 65% of its shoes from supplier A.

(a) Draw a tree diagram to show this information.

(b) Find the probability that a shoe is picked from supplier A given that it is defective.

Answer 1

1)

Let

Adult ticket cost=x

Child's ticket cost=y

According to given statement

5x+3y=108

3x+10y=155

Solve above equations

     15x+9y=324

    15x+50y=775

(-)

---------------------------

     -41y= -451

y=11

Substitute 11 for y in first equation,

5x+3 (11)=108

5x=75

x=15

Therefore, cost of adult ticket is $15 and cost of child's ticket is  is $11.

 

 

 

 

 

Answer 2

2)

Let

fruit juice cost=x

Vanila thick cost=y

According to given statement

y=x+2

5x+3y=$30

Substitute x+2 for y in above relation.

5x+3(x+2)=$30

     8x=24

   x=3

Substitute 3 for x in first equation,

y=3+2

 =5