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13.2 Solving problems

13.2 Solving problems

You can use equations to solve simple number problems.

Worked example 13.2
Xavier thinks of a number. He doubles the number. He adds 3. He doubles again. The answer is 70.
What number did he think of?

Call the number N. You can use any letter.
2N + 3 Double it and add 3.
2(2N + 3) = 70 Double 2N + 3 is 70. Now solve the equation.
2N + 3 = 35 Divide both sides by 2.
2N = 32 Subtract 3.
N = 16 The number is 16.

) Exercise 13.2

1 Lynn picks three numbers and calls them a, a + 2 and a + 4.
a Find the difference between the largest and smallest numbers.
b The sum of the three numbers is 100. Write down an equation to show this.

c Solve your equation to find the value of a.
d Write down the values of the three numbers.
x cm
2 The length of this rectangle is x cm.
a The width of the rectangle is 2 cm less than the length.
Write down an expression for the width of the rectangle, in centimetres.
b The perimeter of the rectangle is 84 cm. Write down an equation to show this.
c Solve the equation.
d Find the area of the rectangle.

3 3N and 3N + 3 are two consecutive multiples of three.
a The sum of the two numbers is 141. Write down an equation to show this.

b Solve the equation to find the value of N
c Work out the values of the two initial numbers.
4 Adeline is A years old.
a Write down an expression for:
i Adeline’s age in 10 years’ time In 10 years’ time, I
ii Adeline’s age 6 years ago. shall be twice as old
b Write down an equation for A. as I was 6 years ago.

c Solve the equation to find Adeline’s age now.
5 The sides of a triangle, in centimetres, are x, 2x − 3 and 2x + 5. The perimeter of the triangle is 57 cm.
a Write down an equation for x.
b Work out the lengths of the three sides of the triangle.

6 This equilateral triangle and square have equal perimeters. a + 7 cm
a Write down an equation to show this. a + 3 cm
b Solve the equation.
c Find the lengths of the sides of the shapes. 3a cm

13 Equations and inequalities 127