Question

The sum of two numbers is 58. The first number is 8 less than half the second number. Let c represent the first number. Let d represent the second number. Which statements about solving for the two numbers are true? Check all that apply.

Answer 1

ABGH

Explanation:

Answer 2

Answer : The true statements are:

The equation
`c+d=58` represents the sum of two numbers.

The equation
`c=(d)/(2)-8` represents the relationship between the two numbers.

The number c is, 14

The number d is, 44

Step-by-step explanation :

Given:

Let 'c' represent the first number. Let 'd' represent the second number.

The sum of two numbers is 58. The equation will be:

`c+d=58` .........(1)

The first number is 8 less than half the second number. The equation will be:

`c=(d)/(2)-8` .........(2)

Now by solving the two equations, we get the value of c and d.

As,
`c+d=58`

or,
`c=58-d` ..........(3)

Now put equation 3 in 2, we get the value of d.

`58-d=(d)/(2)-8`

`58-d=(d-16)/(2)`

`2(58-d)=d-16`

`116-2d=d-16`

`3d=132`

`d=44`

Now put the value of 'd' in equation 3, we get the value of 'c'.

`c=58-d`

`c=58-44`

`c=14`

Thus, the value of c and d is, 14 and 44 respectively.