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

Answer : The true statements are:

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

The equation $c=\frac{d}{2}-8$ 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:

$c=\frac{d}{2}-8$      .........(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.

$58-d=\frac{d}{2}-8$

$58-d=\frac{d-16}{2}$

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

$116-2d=d-16$

$3d=132$

$d=44$

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.

Answer 2

Answer:

The two number as 23 and 35

Step-by-step explanation:

The sum of two numbers = x + y=58

The larger number is 12 more than the smaller number= So, pick a letter, I choose X, Now add 12 to x.

You would write that as: x +12 and that is what you will replace the "y" with below.

So, y= x + 12,

The replacement result would be:   x + x + 12=58

X+X=2X or 2 times x

So next just put that 2X into the equation like this: 2X + 12 = 58

Now Subtract 12 from BOTH sides of the equal sign.

What is left is 2X = 46

Because 2x is a multiplication problem, you must do the opposite to remove it by dividing both sides of the "=" by 2.

So, 2/2=1 and any number times 1 is that original number. So will just write X

Therefore that leaves X by itself on the left side of the = sign. And now divide 46/2= 23

So, x=46/2

The result is x=23.

We know the larger number or "y" is 12 more than x (the smaller number). So Replace X with 23 and you get:

y=23 + 12 = 35 Therefore y= 35

So x= 23 and Y = 35

The numbers are 23 and 35.