Cambridge International Mathematics

Algebra (Equations and inequalities) (Chapter 3) 85

3 Write an equation for each of the following:

a Peter is buying some outdoor furniture for his patio. Tables cost$40each and chairs cost$25

each. Peter buys 10 items of furniture at a total cost of$280. (Let the number of tables purchased

bet.)

b Pencils cost 40 pence each and erasers cost 70 pence

each. If I purchase three fewer erasers than pencils, the

total cost will be$ 3 : 40. (Let the variableprepresent

the number of pencils purchased.)

c A group of friends went to a cafe for tea and coffee. Tea

costsE 2 : 50 and coffee costsE 3 : 60. The number of people

who ordered coffee was twice the number who ordered

tea, and the total bill wasE 29 : 10. (Let the number of

people who ordered tea bet.)

PROBLEM SOLVING METHOD

² Identify the unknown quantity and allocate a variable to it.

² Decide which operations are involved.

² Translate the problem into a linear equation and check that your translation is correct.

² Solve the linear equation by isolating the variable.

² Check that your solution does satisfy the original problem.

² Write your answer in sentence form.

Example 14 Self Tutor

The sum of 3 consecutive even integers is 132. Find the smallest integer.

Letxbe the smallest even integer

) the next is x+2and the largest is x+4:

So, x+(x+2)+(x+ 4) = 132 ftheir sum is 132 g

) 3 x+ 6 = 132

) 3 x+6¡ 6 = 132¡ 6 fsubtracting 6 from both sidesg

) 3 x= 126

)

3 x

3

=

126

3

) x=42 ) the smallest integer is 42 :

D PROBLEM SOLVING USING EQUATIONS

fgdividing both sides by 3

IGCSE01

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Y:\HAESE\IGCSE01\IG01_03\085IGCSE01_03.CDR Wednesday, 17 September 2008 9:20:25 AM PETER