Question

The sum of two numbers is 4 1/8 and their difference is 7/8. What are the numbers? Explain how you found your answer.

Answer 1

`x=3`

`y=(17)/(8)`

Explanation:

Firstly, we have to transform what is written in words to equations.

The sum of two numbers is 41/8

If we call the unknown numbers as
`x` and
`y`, we will have:

`x+y=(41)/(8)` (1)

Their difference is 7/8

`x-y=(7)/(8)` (2)

Now we have a system with two equations and two unknowns. Let's solve it.

Isolating
`x` from (1):

`x=(41)/(8)-y` (3)

Substituting (3) in (2):

`(41)/(8)-y-y=(7)/(8)` (4)

Isolating
`y`:

`(41)/(8)-(7)/(8)=2y`

`y=(34)/(16)=(17)/(8)` (5) This is the value of y

Substituting (5) in (1):

`x+(17)/(8)=(41)/(8)` (6)

Finding
`x`:

`x=(41)/(8)-(17)/(8)`

`x=3` (7) This is the value of x