Question

Two numbers total 63 and have a difference of 31. Find the two numbers

Answer 1

Answer: 47 and 16

Step-by-step explanation:

- Make Two Equations

x + y = 63

x - y = 31

- Set one of the equations equal to one of the variables

x + y = 63

x = 31 + y

- Substitute the equation back into the other one

(31 + y) + y = 63

31 + 2y = 63

2y = 32

y = 16

- Substitute the answer back into the equation

x + y = 63

x + 16 = 63

x = 47

Answer 2

Answer:

47 and 16

Step-by-step explanation:

Start by writing this question as two equations, lets call the two numbers x and y.

"Two numbers total 63" we can write that as x+y=63

"...and have a difference of 31" we can write that as x-y=31 or y-x=31 or |x-y| = 31 or |y-x| = 31. There a lot of ways to write that.

So lets use y-x=31 as the second equation, you can ignore the other possible ways since it doesn't matter in this problem to use absolute value

Using subsitution solve for x using x+y = 63,  x = -y + 63

Plug that into the other equation, -y+63-y=31

−2y+63=31 (Simplify both sides of the equation)

−2y+63+−63=31+−63 (Add -63 to both sides)

−2y=−32

y=16 (Divide both sides by -2 to get Y by itself)

We solved for Y(of of the numbers), now for X (the other number)

Substitute 16 for y in x= − y + 63:

x=−y+63

x=−16+63

x=47