Page 54 - 新思维数学学生用书8 样章

2.5 Constructing and solving equations

8 Work out the value of x and y in each diagram. All measurements are in centimetres.

Show how to check your answers are correct.
a 5x − 3 b 3x + 1

2(y + 3) 20 4y + 5 2y + 15

37
2(x + 5)
c 5x − 3 d 25

16 8(y − 1)
3y + 16 8y − 4
x + 17
3x + 11 4

9 Work in a group of three or four. For each part of this question:
i Write an equation to represent the problem.
ii Compare the equation you have written with the equations written by the other
members of your group. Decide who has written the correct equation in the easiest

way.
iii Solve the equation you chose in part ii.
a Emily thinks of a number. She multiplies it by 3 then adds 8.

The answer is 23. What number did she think of?
b Anders thinks of a number. He divides it by 4 then subtracts 8. The answer is 5. What
number did he think of?
c Sasha thinks of a number. She multiplies it by 5 then subtracts 4. The answer is the same
as 2 times the number plus 20.

What number did Sasha think of?
d Jake thinks of a number. He adds 5 then multiplies the result
by 2. The answer is the same as 5 times the number take away 14. What number did Jake

think of?
Tip
10 The diagram shows the sizes of the angles in a triangle.
a Write an equation to 6n ° represent the problem.
Start by writing an
b Solve your equation to find the value of n.
expression for the
c Work out the size of each of the angles in the
total of the angles
( 2n + 5 ° ) ( n − 5) °
triangle. in the triangle.
Then write an
equation. Use the
fact that the angles

in a triangle add up
to …

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