Question

The sum of two numbers is 16. Their difference is 6. What are the numbers? What is their product?

Answer 1

`11 xx 5= 55`

Explanation:

Define the two numbers first.

Let the smaller number be x, then the bigger number is (16-x).

`(16-x)-x = 6" "larr` bigger - smaller = 6

`16-x-x = 6`

`16-6 = 2x`

`10 =2x`

`5 = x`

the numbers are 5 and 11.

Check:
`11+5 = 16`

`11-5 = 6`

`11xx5 = 55`

Answer 2

The two numbers are 11 and 5

The product is `11xx5=55`

Explanation:

`color(blue)("Determine the two numbers")`

Let the first number be `a`
Let the second number be `b`

`a + b=16` ..................Equation(1)
`a-b=6` ......................Equation(2)

Adding the two equations gives

`2a=22`

Divide both sides by 2

`color(green)(a=11)`..........................Equation(3)
'.................................................................................................
Substitute equation(3) into one of (1) or (2)
I chose equation(1)

`color(brown)(a + b=16)color(purple)(" "->" "11+b=16)`

Subtract 11 from both sides

`color(green)(b=5)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Determine the product")`

Product `-> axxb =11xx5color(green)(=55)`