Question

Variable c is 5 more than variable
a. Variable c is also 3 less than variable
a. Which pair of equations best models the relationship between c and a?

c = a − 5
c = a + 3

a = c + 5
a = 3c − 3

a = c − 5
a = 3c + 3

c = a + 5
c = a − 3

Answer 1

First, let us restate the given conditions

c is 5 more than variable a ( c = a + 5)
c is also three less than variable a (c = a - 3)

Now, lets look at the answer choices and or given
c = a − 5 
c = a + 3
Here, c is 5 less than "a"...so automatically disqualified

a = c + 5
a = 3c − 3 
Here, we have to get "C" by itself in both top and bottom equation.
So,
Simplified version :
c = a - 5
Here, c is 5 less than "a"...so automatically disqualified


a = c − 5
a = 3c + 3
Here also, we have to get "C" by itself in both top and bottom equation.
So, 
simplified version:
c = a + 5
Here, c is 5 more than "a"...so we continue
c = (a - 3) / 3
Here, c is 3 less than "a" divided by 3 . So, this is not correct

c = a + 5
c = a − 3
Here, c is 5 more than "A"
Also, c is 3 less than "a"
Which satisfies the given.

 So, our answer is going to be the last one:
 
 c = a + 5
 c = a - 3

Answer 2

The pair of equations best models the relationship between c and a is option D :  c = a + 5,  c = a - 3

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given conditions are;

c is 5 more than variable a.

( c = a + 5)

c is also three less than variable a.

(c = a - 3)

Now, lets look at the answer choices,

c = a − 5

c = a + 3

Here, c is 5 less than "a". so it will be automatically disqualified.

a = c + 5

a = 3c − 3

So,

Simplified version :

c = a - 5

Here, c is 5 less than "a"..so it will be automatically disqualified.

a = c − 5

a = 3c + 3

Here also, we have to get "c" by itself in both top and bottom equation.

So,

Simplified version:

c = a + 5

Here, c is 5 more than "a"

c = (a - 3) / 3

thus, c is 3 less than "a" divided by 3 . So, this is not correct.

c = a + 5

c = a − 3

Here, c is 5 more than "A"

Also, c is 3 less than "a"

So, Which satisfies the given.

So, our answer is going to be the option D :

c = a + 5

c = a - 3

Learn more about equations here;

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