Question

1. Nine added to thrice a number gives 45.Find the number.

2. The sum of three consecutive numbers is 39 . Find the numbers. ​

Answer 1

Step-by-step explanation:

1.3x+9=45

3x=45-9

3x=36

x=36/3

x=12

2.Let the three consecutive numbers be x,x+1,x+2

x+x+1+x+2=39

3x+3=39

3x=39-3

3x=36

x=36/3

x=12

Answer 2

Question:

1. Nine added to trice a number gives 45. Find the number.
2. The sum of three consecutive numbers is 39. Find the numbers.

Solution:

     1. Let the number be x. Then,

$\because \sf{3x+9=45}\\\implies \mathtt{3x=45-9}\\\implies \mathtt{3x=36}\\\implies \mathtt{x=\frac{36}{3}}\\\implies \sf{x=12}$

Hence the number is 12.

   

     2. Let the numbers be x, (x+1), (x+2). Then,

$\because \sf{x+(x+1)+(x+2)=39}\\\implies \mathtt{x+x+1+x+2=39}\\\implies \mathtt{3x+3=39}\\\implies \mathtt{3x=39-3}\\\implies \mathtt{3x=36}\\\implies \mathtt{x=\frac{36}{3}}\\\implies \sf{x=12}$

Hence, 1st number = 12

            2nd number = 12+1 = 13

            3rd number = 12+2 = 14

Extra Information:

• An equation is a statement of equality which contains one or more unknown variables.
• Any value of the variable which makes the equation true is called solution/root of the equation.

• Transposition is a method in which any term of an equation may be taken from LHS to RHS(or RHS to LHS)with a change in its sign.