Question

The sum of two numbers is 70. Their difference is two less than the smaller number. What are the numbers?

Answer 1

24 and 46

Explanation:

Let x be the smaller number

x+y =70

y-x =x-2

Add x to each side

y-x+x = x+x-2

y = 2x-2

Substitute into the first equation

x+y =70

x+ (2x-2) =70

Combine like terms

3x-2=70

Add 2 to each side

3x-2+2 = 70+2

3x = 72

Divide by 3

3x/3 =72/3

x = 24

y = 2x-2

y = 2(24)-2

y =48-2

y = 46

Answer 2

Two numbers are x = 46 and y = 24

Explanation:

Let the two numbers be x and y , where x > y.

According to given problem,

{sum of two numbers x and y}

x + y = 70 ...................(1)

And

{difference between x and y is two less than the smaller number i.e. y}

x - y = y - 2 ..................(2)

From equation (2) we can write ,

x - y = y - 2

x = 2y - 2 ...................(3)

Plug x =2y - 2 in equation (1).

x + y = 70

(2y - 2) + y = 70

3y - 2 = 70

3y = 72

y = 72/3 = 24

Hence we get y = 24 ,

then x =70 - 24 = 46