The sum of two numbers is 36. Twice the first number minus the second is 6. What are the numbers?

Answer 1

Let's say the first number is x and the second number is y.

"The sum of two numbers is 36" can be translated to the following algebraic equation:

x + y = 36

"Twice the first number minus the second is 6" can be translated to:

2x - y = 6

We now have two equations, two unknowns. We can use Elimination to solve. If you add the two equations together, the y goes away and you're left with:

3x = 42

x = 14

Since 14 is the first number and we know that the sum of the two numbers, x and y, is 36, then the second number must be 22.

x = 14

y = 22

Hope this was helpful.

Answer 2

The key on this type of question is to use the information to set up equations. On this one we have

x + y = 36 because the sum of the 2 numbers is 36

2x - y = 6 because twice the first number minus the second is 6

i would plug the first equation into the second

2x - (36 - x) = 6

3x - 36 = 6

3x = 42

x = 14

meaning that

14 + y = 36

y = 22

Answer 3

let the first number = x and the second = y. We have a system of linear equations so we can set them up as such:

{x+y = 36} #sum of both numbers = 36

{2x-y = 6} #2 times the first number (x) minus the second (y) = 6

*combine like terms; the y will cancel out:

x + y + 2x - y = 42 -> 3x = 42; x = 14 *now plug x in to find y*

14 + y = 36; y = 22

check using second equation:

2(14) - 22 = 6 -> 28 - 22 = 6

Answer 4

Hi, this problem can also be solved using a single variable.

As always, let's call one of the numbers x. Since the sum of the numbers is 36, the second number must be 36-x

Now we are ready to setup the equation.

Twice the first number is 2x

The second number, as mentioned above, is 36-x

So we get: 2x - (36-x) = 6

Or 2x - 36 + x = 6

Adding 36 to both sides gives us

3x = 42, so z=42/3 = 14

The other number is 36-x = 36-14 = 22

Does it matter whether we call x or (36-x) the first number? Let's find out.

We could have called x the second number and (36-x) the first number

Then the equation would be: 2(36-x) - x = 6

72 - 2x - x = 6

3x = 72 - 6 = 66

So x is 66/3 = 22

And 36-22 is the other number, 14

So we get the same solution either way! Isn't it cool algebra takes care of it automatically for us!