The second of two numbers is 6 less than 3 times the first. Their sum is 26. Use one variable

Answer 1

For this problem, we need to form two algebraic equations in order to have a system of equations. The first step is to assign variables to the two numbers we need to solve for. Let's call the:

1st number = x

2nd number = y

The problem states that the 2nd number is 6 less than 3 times the first number. From this, we get our first algebraic equation:

y = 3x - 6

The problem also states that the sum of these two numbers is 26. From this, we get our second algebraic equation:

x + y = 26

Our system of equations is:

I) y = 3x - 6

II) x + y = 26

We can find out what the 1st number is by using the substitution method. Substitute the first equation into the second equation:

x + y = 26

x + (3x - 6) = 26 Substitute.

4x - 6 = 26 Combine like terms.

4x = 32 Add 6 to both sides.

x = 8 Divide both sides by 4.

The 1st number is 8.

Next, we can find out what the 2nd number is by substituting 8 into either the first or second algebraic equation. You can choose either one as they will both give the same correct answer. Let's choose the first equation:

y = 3x - 6

y = 3(8) - 6 Substitute.

y = 24 - 6 Multiply.

y = 18 Combine like terms.

The 2nd number is 18.

Answer:

1st number: 8

2nd number: 18

Answer 2

We know that the second number plus the first number equals 26. We know that because the definition of the word sum is the answer we get when we add. We also know that the second number is 6 less (which means subtract 6 from) than a number which happens to be 3 times bigger (this means we must multiply by 3) than the first number. So let us call the first number x. We know that in order to get the second number we must multiply the first number by 3, which will give us 3x. We will then take away (subtract) 6 from 3x, which equals 3x - 6. And the first number, x, plus the second number, 3x - 6, will have a sum of 26: We are now ready to set up our equation and solve for x.

x + (3x - 6) = 26

x + 3x - 6 = 26

4x - 6 = 26

4x -6 +6 = 26 + 6

4x + 0 = 32

4x = 32

4x/4 = 32/4

x = 8

Answer 3

Assume first number is x

Then the second number s 3x-6

You know that their sum is 26. So,

x+(3x-6)=26

4x=32

Then, the first number is

x=32/4=8

And, the second number is

3*8-6=18.

Answer 4

Since we know that we have two numbers, and they are related via the problem, we can assign the unknown number we want as "x". The second of the two numbers can be represented as a transformation of the first number ( notably 3x - 6 ). Using the sum of these two numbers gives...

x + ( 3x - 6 ) = 26

4x - 6 = 26

4x = 32

x = 8

One number is 8 and the other number 3(8) - 6 --> 18