Cambridge International Mathematics

86 Algebra (Equations and inequalities) (Chapter 3)

Example 15 Self Tutor

If twice a number is subtracted from 11 , the result is 4 more than the number.

What is the number?

Letxbe the number,

LHS algebraic expression is 11 ¡ 2 x

RHS algebraic expression is x+4.

) 11 ¡ 2 x=x+4 fthe equationg

) 11 ¡ 2 x+2x=x+4+2x fadding 2 xto both sidesg

) 11 = 3x+4

) 11 ¡ 4 =3x+4¡ 4 fsubtracting 4 from both sidesg

) 7=3x

)

7

3

=

3 x

3

fdividing both sides by 3 g

) x=2^13 So, the number is 213.

Example 16 Self Tutor

Cans of sardines come in two sizes. Small cans cost$2each and large cans cost$3each.

If 15 cans of sardines are bought for a total of$38, how many small cans were purchased?

Size Cost per can Number bought Value

small $2 x $2x

large $3 15 ¡x $3(15¡x)

15 $38

So, 2 x+ 3(15¡x)=38

) 2 x+45¡ 3 x=38 fexpanding bracketsg

) 45 ¡x=38

) 45 ¡x¡ 45 =38¡ 45 fsubtracting 45 from both sidesg

) ¡x=¡ 7

) x=7 So, 7 small cans were bought.

EXERCISE 3D

1 When a number is doubled and the result is increased by 6 , the answer is 20. Find the number.

2 The sum of two consecutive integers is 75. Find the integers.

3 The sum of three consecutive even integers is 54. Find the largest of them.

4 When a number is subtracted from 40 , the result is 14 more than the original number. Find the number.

5 When 22 is subtracted from a number and the result is doubled, the answer is 6 more than the original

number. Find the number.

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Y:\HAESE\IGCSE01\IG01_03\086IGCSE01_03.CDR Friday, 12 September 2008 12:32:52 PM PETER