# Finding solutions to problems with two variables

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## Lesson details

### Key learning points

- In this lesson, we will be discussing how to work systematically to find all possibilities for problems with two variables.

### 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.

Which expression would represent the following problem: The cooking time for roast beef is 30 minutes for every kg plus an additional 15 minutes.

a = 500b + 30

Q2.

Which expression would represent the following problem: The cost of a photo album book is £2.50 for binding and printing with an additional cost of 15p per photograph.

a = 250b + 15

Q3.

Which expression would represent the following problem: A singer makes money from selling music. They pay a one-off fee of £25.00 to Oak-Tunes for marketing and distribution costs and receive 55p for each copy of the album sold.

a = 25 + 0.55

a = 2500 + 55a

Q4.

Instead of writing 5 x a in an algebraic expression, what could I write instead?

5 + a

a5

### 4 Questions

Q1.

3f + g = 15. Which of the following pairs of numbers would work?

f = 2, g = 10

f = 4, g = 2

f = 5, g = 1

Q2.

5a - 2b = 8. Which of the following pairs of numbers would work?

a = 3, b = 2

a = 4, b = 12

a = 5, b = 6

Q3.

3c + 2d = 20. Which pair of numbers does does NOT work with this equation?

c = 2, d = 7

c = 6, d = 1

Q4.

6m - 3n = 15. Which pair of numbers does does NOT work with this equation?

m = 3, n = 1

m = 5, n = 5

m = 7, n = 9