Question

The sum of two numbers is 100 and their difference is 20. What is the value of bigger number?

Answer 1

Value of bigger number is 60, smaller number is 40.

Explanation:

Let the bigger number be x.
x + (x - 20) = 100, as the difference is 20.
Solving for x we get 60, which is the bigger number.

Alternatively, you can draw a bar model to illustrate but i feel algebras faster.

Answer 2

`60`

Explanation:

`"create 2 equations based on the given information"`

`"let x and y be the 2 numbers"`

`"with "x>y`

`rArrx+y=100to(1)larrcolor(blue)"sum of numbers"`

`rArrx-y=20to(2)larrcolor(blue)"difference of numbers"`

`"add (1)" and (2)" term by term"`

`(x+x)+(y-y)=(100+20)`

`rArr2x=120larrcolor(blue)"divide both sides by 2"`

`rArrx=60larrcolor(red)"the larger number"`