Cambridge International Mathematics

Formulae and simultaneous equations (Chapter 7) 165

) 40 x+ 112y= 6960 :::::(3)

¡ 40 x¡ 45 y=¡ 4950 :::::(4)

67 y= 2010 fadding (3) and (4)g

) y=30 fdividing both sides by 67 g

Substituting in (2) gives 8 x+9£30 = 990

) 8 x= 990¡ 270

) 8 x= 720

) x=90 fdividing both sides by 8 g

Check: 5 £90 + 14£30 = 450 + 420 = 870 X

8 £90 + 9£30 = 720 + 270 = 990 X

Thus coconuts cost 90 cents each and bananas cost 30 cents each.

Example 21 Self Tutor

In my pocket I have only 5 -cent and 10 -cent coins. How many of each type of coin do

I have if I have 24 coins altogether and their total value is$1: 55?

Letxbe the number of 5 -cent coins andybe the number of 10 -cent coins.

) x+y=24 ::::::(1) fthe total number of coinsg

and 5 x+10y= 155 ::::::(2) fthe total value of coinsg

Multiplying (1) by¡ 5 gives ¡ 5 x¡ 5 y=¡ 120 ::::::(3)

5 x+10y= 155 ::::::(2)

) 5 y=35 fadding (3) and (2)g

) y=7 fdividing both sides by 5 g

Substituting into (1) gives x+7=24

) x=17

Check: 17 + 7 = 24 X

5 £17 + 10£7 = 85 + 70 = 155 X

Thus I have 17 five cent coins and 7 ten cent coins.

EXERCISE 7F

1 The sum of two numbers is 49 and their difference is 19. Find the numbers.

2 The average of two numbers is 43 and their difference is 16. Find the numbers.

3 The average of two numbers is 20. If one of the numbers is doubled and the other is trebled, the average

increases to 52. Find the numbers.

4 Four nectarines and three peaches cost$ 2 : 90 , and three nectarines and a peach cost$ 1 : 90. Find the

cost of each fruit.

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Y:\HAESE\IGCSE01\IG01_07\165IGCSE01_07.CDR Monday, 15 September 2008 4:52:57 PM PETER