The sum of two numbers is 6. One number is 14 more than the other one. Find the numbers.

Answer 1

Let's use the first sentence to set up our variables.

If the sum of two numbers is 6, our numbers can be represented by x and 6 - x.

It doesn't matter what you label them as so let's call x our first number and 6 - x our second number.

Now we can use the second sentence to set up our equation.

One number, that's x, is, equals, 14 more than the other, that's (6 - x) + 14.

So we have the equation x = 6 - x + 14 or x = -x + 20.

Now add x to both sides to get 2x = 20.

Now just divide both sides by 2 so x = 10.

Now plug a 10 back in for x to find our second number which is -4.

So our answers are 10 and -4.

Answer 2

Let x = number1

Let y = number2

Given:

x + y = 6

x = y + 14

Substitute for x:

( y + 14 ) + y = 6

Simplify:

2y + 14 = 6

Isolate y:

subtract 14 from both sides of equation

2y = -8

Solve for y: (divide both sides by 2)

y = -4

substitute in one of the givens: (solve for x)

x + y = 6

x + -4 = 6 (add -4 to both sides of the equation)

x = 10

Solution:

x = 10, y = -4

x is 14 more than y