Question

The sum of two numbers is 12 Their difference is 4. How do you find the numbers?

Answer 1

`8" and " 4`

Explanation:

Let the 2 numbers be x and y with x > y

`rArrxcolor(red)(+y)=12to(1)larr"sum of 2 numbers"`

`rArrxcolor(red)(-y)=4to(2)larr" difference of numbers"`

Adding the 2 equations, term by term on both sides, will eliminate y leaving an equation in x that we can solve.

`rArr(1)+(2)" gives"`

`(x+x)+(color(red)(-y+y))=(4+12)`

`rArr2x=16`

divide both sides by 2

`(cancel(2) x)/cancel(2)=16/2`

`rArrx=8`

Substitute this value into equation ( 1 ) and solve for y

`rArr8+y=12`

`rArry=12-8=4`

`"Thus the 2 numbers are " 8" and " 4`

Answer 2

`a=4`
`b=8`

Explanation:

let these two numbers be `a` and `b`.

`a+b=12`
`a-b=4`

if you add the two equations:

`a+b=12`
`a-b=4`

`2a+0 = 8`
`2a = 8`

divide by `2`:
`a = 4`

substitute:
`a+b = 12`
`4+b=12`
`b=12-4`
`=8`

`a=4`
`b=8`

`8+4=12`
`8-4=4`

Answer 3

There are two numbers so you need two equations. Solve for one variable ( number) and then substitute and solve for the other.

`x = 8 and y = 4`

Explanation:

Let `x` equal one number and `y` the other number.

One equation would be the sum of the numbers.

`x + y = 12`

the other equation would be the difference of the two numbers

`x-y = 4" "`

Now add the two equations

`x +y = 12 " " and " "x -y = 4" "`(adding `+ y and -y = 0`)

so `2x = 16" "` Now divide both sides by 2

`(2x)/2 = 16/2" "` This gives

`x = 8` Now substitute x into one of the equations and solve for y

`8 + y =12" "` subtract 8 from both sides

`8 -8 +y = 12 -8 " "` This gives

`y = 4" "` Put values into the second equation to check

`8 -4 = 4`

`4 = 4" "` check

`x = 8 and y = 4`

Answer 4

The numbers are `4 and 8`

Explanation:

Questions which involve two or more numbers can be done using one variable to define them all.

Let the smaller number be `color(red)(x)`.

The difference between the numbers is `4`.

The other number is `color(blue)(x+4)`

Their sum is `12`

`color(red)(x) +color(blue)(x+4) =12`

`2x = 12-4`

`2x = 8`

`x =4`

`:. x+4 = 8`

The numbers are `4 and 8`