Making Equations (2)
In each of the following, form an equation or an inequation, and use it to solve
the problem.
1. A whole number is doubled and 13 is added. The result is 37.
What is the number ?
2. A whole number is multiplied by 4 and 3 is subtracted from the product. The
result is 17. What is the number ?
3. The length of a rectangle is (x + 3) mm and the breadth is x mm.
a Write an expression in terms of x for the perimeter, in its simplest form
b If the perimeter is 30 mm, find x
c What are the dimensions of the rectangle ?
4. The length of a rectangle is (2x – 5) cm and the breadth is (x + 1) cm.
a Write an expression in terms of x for the perimeter, in its simplest form
b Given that the perimeter is 46 cm, find the value of x
c Find the length, breadth and area of the rectangle.
5. The sides of a triangle are y cm, (y + 2) cm and (y – 3) cm long.
a Write an expression in terms of y for the perimeter, in its simplest form
b If the perimeter is 23 cm, find the value of y
c State the length of each side of the triangle.
6. The angles of a triangle are 90°, (x + 15)° and (x – 15)°
a Find the sum of the angles in terms of x in its simplest form
b Form an equation in x and solve it
c State the size of each angle of the triangle.
7. The angles of a triangle are 4x°, (3x + 1)° and (2x – 1)°
a Find the sum of the angles in terms of x in its simplest form
b Form an equation in x and solve it
c State the size of each angle of the triangle.
Making Equations (2)
(continued)
8. The sides of a triangle are (x + 1) cm, (x – 3) cm and 12 cm.
Form an inequation in x and find the least integral value of x.
9. One diagonal of a rectangle is (8x + 4) cm and the other is (4x + 8) cm.
Find the length of each diagonal
10. The length of one side of a rectangle is (2x + 3) cm and the breadth is 5 cm.
If the area is 255 cm², find the dimensions of the rectangle.
11. The length of one side of a rectangle is (4x + 1) cm and the breadth is 8 cm.
If the area is 312 cm², find the dimensions of the rectangle.
12. The equal sides of an isosceles triangle are each twice the length of the third side.
The perimeter is 60 mm. Find the lengths of the sides of the triangle.
13. One diagonal of a kite is (2x + 3) m long and the other is (x + 7) m long.
If the first diagonal is longer than the second, what can be said about x ?
14. The sum of four consecutive whole numbers is 110. What are the numbers ?
15. The sum of three consecutive even numbers is 228. What are the numbers ?
16. Find the integers that satisfy both of the following inequations :a 8x – 3 > 5x – 9
b 7x – 2 < 3(x + 6)
Making Equations (2) Solutions
1.
Let the number be x
=> 2x + 13 = 37
=> 2x = 24
=> x = 12
2.
Let the number be x
=> 4x – 3 = 17
=> 4x = 20
=> x = 5
3.
4.
5.
6.
7.
8.
9.
a 4x + 6 mm
b 4x + 6 = 30
=> 4x = 24
=> x = 6
c L = 9 mm B = 6 mm
a 6x – 8 cm
b 6x – 8 = 46
=> 6x = 54
=> x = 9
c L = 13 cm B = 10 cm
a 3y – 1 cm
b 3y – 1 = 23
=> 3y = 24
=> y = 8
c Sides:- 8 cm, 10 cm, 5 cm.
a (2x + 90)°
b 2x + 90 = 180
=> 2x = 90
=> x = 45
c Angles are 90°, 60°, 30°
a 9x°
b 9x = 180
=> x = 20
c Angles are 80°, 61°, 39°
(x + 1) + (x – 3) > 12
=> 2x – 2 > 12
=> 2x > 12
=> x > 6
Least integral value of x is 6
8x + 4 = 4x + 8
=> 8x = 4x + 4
=> 4x = 4
=> x = 1
Length of each diagonal = 12 cm
10.
5(2x + 3) = 255
=> 2x + 3 = 51
=> 2x = 48
=> x = 24
L = 51 cm B = 5 cm
11.
8(4x + 1) = 312
=> 4x + 1 = 39
=> 4x = 38
=> x = 9·5
L = 39 cm B = 8 cm
12.
Let the length of the shortest side
be x cm
=> 2x + 2x + x = 60
=> 5x = 60
=> x = 12
Lengths of the sides are :12 cm, 24 cm, 24 cm
13.
2x + 3 > x + 7
=> 2x > x + 4
=> x > 4
14.
Let the numbers be :x, x + 1, x + 2, x + 3
=> 4x + 6 = 110
=> 4x = 104
=> x = 26
The numbers are 26, 27, 28, 29
15.
Let the numbers be x, x + 2, x + 4
=> 3x + 6 = 228
=> 3x = 222
=> x = 74
The numbers are 74, 76, 78
16.
a 8x – 3 > 5x – 9
=> 8x > 5x – 6
=> 3x > –6
=> x > –2
b
=>
=>
=>
=>
7x – 2 < 3(x + 6)
7x – 2 < 3x + 18
7x < 3x + 20
4x < 20
x < 5
Solution Set = {–1, 0, 1, 2, 3, 4}