1. Word Problems
Round 3

2. Sarah, Amy and Liam stand on some weighing scales two at a time.
                                                        
Here are the measurements:
Sarah and Amy              71kg
Sarah and Liam             75kg
Liam and Amy               80kg
How much does Liam weigh?

3. Here is information about pupils in a school.
•     The total number of pupils is 300
•     260 of the pupils do not wear glasses.
•     A quarter of the pupils who do wear glasses are boys.
•     There are 20 more boys than girls. Use the information to fill in the missing numbers in the table below.
Number who do wear glasses
Number who do not wear glasses
Total
Number of boys
Number of girls
300

4. Liam thinks of two numbers. 
When he multiplies the two numbers together, he gets 999.
The difference between the two numbers is 10.
The two numbers total a square number.
What were the numbers Liam started with?

5. Emily has £5 to spend on peaches.
She decides to buy only small peaches or only large peaches.
Small peaches 15p each
How many more small peaches than large peaches can she buy for £5?
Large peaches 25p each

6. Emily had a bag of cherries.
She ate 10 cherries, then gave half of what she had left to Liam.
Liam ate 10 of his cherries, then gave half of what he had left to Amy.
Amy got 5 cherries.
How many cherries did Emily have in her bag at the start?

7. A white square is painted in one corner of a grey square.
Each side of the white square is half the length of a side of the grey square.
12cm
What is the area of the grey section?
12cm

8. Liam and Emily each bought identical T-shirts from the same shop.
Liam bought his on Monday when there was 20% off the original price.
Emily bought hers on Friday when there was 25% off the original price.
Liam paid 49p more then Emily.
What was the original price of the T-shirt?

9. This diagram shows two identical squares on coordinate axes.y B
Write the coordinates of point A and point B. A x
(17, 3)
(27, 3)

10. This is what food costs at Franco’s café.
1 curry and 1 tea cost £4.50.
2 curries and 2 puddings cost £11.
1 pudding and 2 teas cost £2.80
What does each item cost on its own?

11. r t The diagram shows four identical isosceles triangles.
What are the sizes of angles r and t?
36o

12. Liam has an ordinary pack of cards with the face cards (Jacks, Queens and Kings) removed. After shuffling them, he turns over TEN cards, adding the total as he goes. If the total comes to 85, what will the total of the remaining 30 cards be?

13. The diameter of a large circle is 21cm.
Five large circles and seven small circles fit exactly inside this rectangle.
? cm
21cm
The diameter of a large circle is 21cm.
         
What is the diameter of a small circle?

14. Liam has four identical right angled triangles
26cm
24cm
10cm
He uses them to make a star
What is the perimeter of the star?

15. The diagram shows a blue square of side length 20 cm.
Inside the square are 8 congruent trapeziums and a red square.
The side length of the red square is 10 cm.
20cm
What is the area of one of the trapeziums?

16. Mr Robson is making jam to sell at the school fair.
Strawberries cost
£6.50 per kg.
Sugar costs
89p per kg.
10 glass jars cost £7.90
He uses 12 kg of strawberries and 10 kg of sugar to make 20 jars full of jam.
Calculate the total cost to make 20 jars full of jam.

17. That is the end of Round 3…
1 member of each team please give your team’s answer sheet to the marker.
You now have 10 minutes to finish answering the puzzles before the end of the competition.
Each correctly completed puzzle will earn your team an extra 3 points.