The difference of two numbers is 12, and the sum of the two numbers is 40. What are the two numbers?

Question

The difference of two numbers is 12, and the sum of the two numbers is 40. What are the two numbers?

 

Answer 1

X+Y=40

X-Y= 12

Then solve for X in the first equation. That gives X= 40-Y. Substitute for X in the second equation: 40-Y-Y=12.

Then Y= 14, and X= 26

 

Ali Zendedel Haghighi 

Answer 2

Hi Ethan,

 

Let's begin by assigning letters to represent our two numbers:

    x = 1st number

    y = 2nd number

 

Next, let's write two equations which we can use to solve for our two numbers:

    Equation #1 (difference of the two numbers):

        x - y = 12

    Equation #2 (sum of the two numbers):

        x + y = 40

 

Next, let's add Equation #1 to Equation #2 to solve for x (1st number):

    (x + x) + (-y + y) = 12 + 40

    2x + 0 = 52

    2x = 52

    x = 52/2

    x = 26 (1st number)

 

Next, let's plug in our answer for x (1st number) into Equation #1 and solve for y (2nd number):

    x - y = 12

    26 - y = 12

    -y = 12 - 26

    -y = -14

    (-1)(-y) = (-1)(-14)

    y = 14 (2nd number)

 

Finally, let's verify both numbers by plugging them both into Equation #2 to check that the equation is true:

    x + y = 40

    26 + 14 = 40

    40 = 40 (equation is true)

 

Since Equation #2 has been been proven true with our two numbers, we are confident that our two numbers are correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan. 

Answer 3

Let us call the numbers x and y.

Without loss of generality, we can assume that x is the larger of the two.

That means that     x - y = 12

Moreover,              x + y = 40

If we add these equations to each other, the y's will cancel out and we will have

                                 2x = 52
                                   x = 26

Accordingly,

                            26 + y = 40
                                   y = 14

Check:
26 - 14 = 12    √
26 + 14 = 40   √