The Hampton School cheerleading squad is made up of four boys: Tim, Michael, Mark and Daniel, and four girls: Marta, Hannah, Joanna and Caroline.
For the cup final, a cheer team of three boys and two girls has to be chosen. However, Mark will not be in the team if Caroline is picked and Marta will not be in the team if Michael is picked.
In how many ways could a cheer team be chosen for the cup final?

Answer:
8

Well done if you got the correct answers!

Well done to all those who took part in this term’s competition! More Maths Wizard problems will be posted every week during the summer holidays.

Maths Wizard will be back on Monday 9 September 2019!

1. The Maths Wizard loves to play games. In one such game you can score either 5, 8 or 12 points each go. What is the highest score that is impossible to achieve?

Answer: 19

2. In a training session, Marta takes three strides to cover 10m while Hannah takes four strides to cover 12m. How far apart are Marta and Hannah after they have both taken 300 strides?

Answer:

Marta: 300/3 = 100
10 x 100 = 1000 metres travelled
Hannah: 300/4 = 75
12 x 75 = 900 metres travelled
Difference = 1000 – 900 = 100 metres

3. Hannah needs to arrive for a meeting at London Waterloo Station at 0830. It takes her 3 minutes to walk to the bus stop, the bus takes 7 minutes to travel to Windsor and Eton Riverside Station, it then takes her 2 minutes to walk from the bus to the platform, and the train takes 35 minutes to arrive into London Waterloo Station. The buses are unreliable and can run up to 5 minutes late, the trains run on time. Use the bus and train timetable below to work out the latest time she should leave her house to guarantee she is not late for her meeting. 

Answer:  Hannah should leave at 0732 and will arrive at exactly 0830.

4. The Maths Wizard has a square garden with 52 posts positioned every 4 metres around the edge.
What is the area of his garden (in square metres)?

Answer:
52 x 4 = 13
Therefore, there are 13 posts for each side of the square garden
13 x 4 = 52 metres
Therefore, each side of the square garden measure 52 metres
Area = width x length = 52 x 52 = 2704 square metres

5. Hannah and Daniel each have the same amount of money.
If Hannah spends £10 and Daniel £20 then Hannah has three times as much as Daniel.
If Hannah spends £15 and Daniel £20 then Hannah has twice as much as Daniel.
How much money do they have altogether?

Answer:
Let a = Hannah’s money and therefore a = Daniel’s money
a – 10 = 3 (a – 20)
a – 10 = 3 a – 60
(add 60 to each side of the equation)
a + 50 = 3a
(subtract a from each side of the equation)
50 = 2a
a = 25
Therefore Hannah and Daniel have £25 each so £50 altogether

6. Mrs Clarke bought cakes for her class.
If everyone in the class had 2 cakes each there would be 10 left over.
If everyone had 3 cakes each there would be 15 buns short.
How many cakes did Mrs Clarke buy?

Answer:
Let b = number of pupils in a class
2b + 10 = 3b – 15
(add 15 to each side of the equation)
2b + 25 = 3b
(subtract 2b from each side of the equation)
b = 25
Therefore there are 25 pupils in the class
Cakes = 2 x 25 + 10 = 60
Mrs Clarke bought 60 cakes for her class

7. If A + Z + Z = 19
R + A + M + A = 18
T + A + Z = 18 and T = 5
where each letter represents a different digit, what is the value of:
R + A + Z + Z + A + M + A + T + A + Z + Z

8. If the following pattern were continued, what would be the sum of the numbers at the start and end of the 10th row?
    1
   2 3
  4 5 6
7 8 9 10

9. Marta’s llamas need a new enclosure. She has 800m of fencing available and can only build using straight line sections. Find:
a) the maximum possible area
b) the dimensions of the new enclosure

Answer:
A square 200m by 200m enclosure, with area 40,000m²

10. My famous recipe for apple crumble has only two ingredients: apples and crumble. I need to have 5 parts apple to 3 part crumble for the best possible result. Given that I need to produce a 12kg apple crumble for my guests, how many more kilograms of apples than crumble are required?

Answer:
12kg = 12,000g
So one part would be 12,000/8 = 1,500g
The difference would be two parts, so 1500 x 2 = 3,000g = 3kg

11.In a training session, Marta takes three strides to cover 10m while Hannah takes four strides to cover 12m. How far apart are Marta and Hannah after they have both taken 300 strides?

Answer:
Marta: 300/3 = 100
10 x 100 = 1000 metres travelled
Hannah: 300/4 = 75
12 x 75 = 900 metres travelled
Difference = 1000 – 900 = 100 metres

12. Hannah needs to arrive for a meeting at London Waterloo Station at 0830. It takes her 3 minutes to walk to the bus stop, the bus takes 7 minutes to travel to Windsor and Eton Riverside Station, it then takes her 2 minutes to walk from the bus to the platform, and the train takes 35 minutes to arrive into London Waterloo Station. The buses are unreliable and can run up to 5 minutes late, the trains run on time. Use the bus and train timetable below to work out the latest time she should leave her house to guarantee she is not late for her meeting.

Well done if you got the correct answers!