**Forming Simultaneous Equations**

Starter

Three bananas and one apple cost a total of 65p.

Seven bananas and two apples cost a total of £1.49.

(a) Write down the cost of six bananas and two apples.

(b) Write down the cost of one banana.

(c) Work out the cost of one apple.

Activity

Complete the Simultaneous Scenarios worksheet

Forming and Solving simultaneous equations

Mrs Jones is buying bottles of still and sparkling water.

She buys x bottles of still water and y bottles of sparkling water. Altogether she buys 23 bottles of water.

Still water costs 50p per bottle and sparkling water costs 65p per bottle.

Altogether she spends £13.15.

Write down a pair of simultaneous equations and solve them to find out how many bottles of still water and sparkling water Mrs Jones buys.

L.O. - Form simultaneous equations from problems and solve.

Forming and Solving simultaneous equations

Mrs Jones is buying bottles of still and sparkling water.

She buys x bottles of still water and y bottles of sparkling water. Altogether she buys 23 bottles of water.

Still water costs 50p per bottle and sparkling water costs 65p per bottle.

Altogether she spends £13.15.

Write down a pair of simultaneous equations and solve them to find out how many bottles of still water and sparkling water Mrs Jones buys.

x + y = 23 50x + 50y = 1150

50x + 65y = 1315

15y = 165

x + 11 = 23

y = 11

x = 12

Forming and Solving simultaneous equations

A rectangular shape is made using 12 square tiles placed with equal gaps

between them as shown.

The overall length of the rectangle is 645 mm and the overall width is 475 mm.

Find the length of the tile and the length of the gap.

Forming and Solving simultaneous equations

A rectangular shape is made using 12 square tiles placed with equal gaps

between them as shown.

The overall length of the rectangle is 645 mm and the overall width is 475 mm.

Find the length of the tile and the length of the gap.

4x + 3y = 645

8x + 6y = 1290

3x + 2y = 475

9x + 6y = 1425

x = 135

3(135) + 2y = 475

405 + 2y = 475

2y = 70 y = 35

Starter

Three bananas and one apple cost a total of 65p.

Seven bananas and two apples cost a total of £1.49.

(a) Write down the cost of six bananas and two apples.

£1.30

(b) Write down the cost of one banana.

19p

(c) Work out the cost of one apple.

8p

Plenary

Plenary

4c + 4t = 12

3c = 2t

6c - 4t = 0

10c = 12

c = 1.20

3(1.20) = 2t

3.60 = 2t

t = 1.80

Andrew paid £12 for 4 cups of coffee and 4 cups of tea.

3 cups of coffee cost as much as 2 cups of tea.

Work out the cost of a cup of each drink.

Andrew paid £12 for 4 cups of coffee and 4 cups of tea.

3 cups of coffee cost as much as 2 cups of tea.

Work out the cost of a cup of each drink.

**Activities**

**Activity**

Answers

Answers

**Key**

Examples

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**Worked**

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