Mathematics (5 questions)

Question

1) Jordan and Poppy invest $24,000 in the ratio 7:9.

How much does each person receive?

2) Zac has a 75% chance of winning a tennis tournament. The other three players, Angus, Billy and Connor are equally likely to win. What is the probability that Angus wins the tournament?

3) The numbers 1 to 20 are written on separate cards. One card is chosen at random. What is the probability that the card chosen is a prime number or is divisible by 3?

4) Find the interquartile range of this data:

15, 15, 16, 14, 12, 18, 20, 22, 52, 28

5) Anna sold a camera for $119 at a loss of 30%.

(i)

How much did Anna pay for the camera?

(ii)

What price should Anna sell the camera to make a 20% profit?

Answer 1

24,000 divided in ratio of 7:9

(7/16)24,000 and (9/16)24,000

shares are $10,500 and $13,500

25/3 = 8 1/3 % chance for Angus

2,3,5,7, 11, 13, 17, 19 are the prime numbers between 1 and 20

3,6,9,12,15,18 are the numbers divisible by 3

total numbers prime or divisible by 3 are 13

13/20 = 65% chance of getting a prime or number divisible by 3

119 at a loss of 30%

x -119 = .3x

x-.3x = 119

.7x = 119

x = 119/.7 = $170 = original price before the loss

.3(170) = 51

170-51 = 119

170+.2(170) = 170+34 = $204 price to make 20% profit

52-12 = 40

40/4 = 10

12 to 22

22 to 32

32 to 42

42 to 52