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Chapter 2: Q. 2.31 (page 97)

The sum of two numbers is negative twenty-three. One number is seven less than the other. Find the numbers.

Short Answer

Expert verified

Numbers will be(-8)and (-15).

Step by step solution

01

Step 1. Assume the number,

Let the first number is 'a'.

02

Step 2. Form the first equation.

Statement given, "Sum of two numbers is-23.

Equation for the statement will be,

1st Number + 2nd Number = -23

a+ 2nd Number = -23

Therefore, second number = -23-a

03

Step 3. Form the second equation.

Second statement given in the question states that, "One number is seven less than the other number ".

Equation for the statement will be,

(-23-a)=(a)-7

04

Step 4. Solve the equation,

(-23-a)+7=(a-7)+7(Add 7 to both sides of the equation)

-16-a=a

(-16-a)+a=a+a(Isolate variable 'a'on the right side of the equation)

2a=-16

05

Step 5. Divide both the sides by 2,

a=-8

06

Step 6. Substitute the value of'a' to get the numbers.

1st number =-8

2nd number = role="math" localid="1644180898519" -23-(-8)=-15

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