# Reasoning and problem solving (Part 2)

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## Lesson details

### Key learning points

- In this lesson, we will continue to explore two types of problem in depth, thinking carefully about how to represent each problem in order to help us find a solution.

### Licence

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

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### 4 Questions

Q1.

If 3f + 8 = 20. What is the value of f?

3

5

6

Q2.

Which expression would represent the following problem: The cost of a photo album book is £1.50 for binding and printing with an additional cost of 25p per photograph.

a = 150b + 25

Q3.

a - 2b = 8. Which of the following pairs of numbers would work?

a = 10, b = 4

a = 5, b = 2

a = 8, b = 1

Q4.

A function machine has the rule x = 2y + 1. Where y is the input and x is the output. If we put 4 into the function machine (y = 4) what would come out?

10

11

8

### 6 Questions

Q1.

If 4f - 8 = 20. What is the value of f?

3

5

9

Q2.

Which expression would represent the following problem: A singer makes money from selling music. They pay a one-off fee of £55 to Oak-Tunes for marketing and distribution costs and receive £1 for each copy of the album sold.

a = 55b + 1

Q3.

Instead of writing 7 x a in an algebraic expression, what could I write instead?

7 + a

a7

Q4.

3c + 2d = 30. Which pair of numbers does does NOT work with this equation?

c = 4, d = 9

c = 6, d = 6

c= 2, d = 12

Q5.

Kate's age now is a multiple of three. In two years' time, her age will be a prime number. Which of the following could be her age?

28

29

30

Q6.

Sam's age now is a multiple of four. In four years' time, her age will be a square number. Which of the following could be her age?

20

21

36