Cambridge International Mathematics

84 Algebra (Equations and inequalities) (Chapter 3)

With practice you will find that you can combine the steps, but you should note:

² the mathematical sentence you form must be an accurate translation of the information

² for these types of problems, you must have only one variable in your equation.

Example 12 Self Tutor

Translate into an equation: “The sum of 2 consecutive even integers is 34 .”

Let the smaller even integer bex.

) the next even integer is x+2.

So, x+(x+2)=34 is the equation.

Example 13 Self Tutor

Apples cost 13 cents each and oranges cost 11 cents each.

If I buy 5 more apples than oranges and the total cost of the apples and oranges is$2: 33 , write a

linear equation involving the total cost.

Type of fruit Number of pieces of fruit Cost per piece of fruit Total cost

oranges x 11 cents 11 xcents

apples x+5 13 cents 13(x+5)cents

233 cents

From the table we know the total cost, and so 11 x+ 13(x+ 5) = 233:

EXERCISE 3C

1 Translate into linear equations, butdo not solve:

a When a number is increased by 6 , the answer is 13.

b When a number is decreased by 5 , the result is¡ 4.

c A number is doubled and 7 is added. The result is 1.

d When a number is decreased by 1 and the resulting number is halved, the answer is 45.

e Three times a number is equal to 17 minus the number.

f Five times a number is 2 more than the number.

2 Translate into equations, butdo not solve:

a The sum of two consecutive integers is 33.

b The sum of 3 consecutive integers is 102.

c The sum of two consecutive odd integers is 52.

d The sum of 3 consecutive odd integers is 69.

IGCSE01

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Y:\HAESE\IGCSE01\IG01_03\084IGCSE01_03.CDR Friday, 12 September 2008 12:22:33 PM PETER