Question

Solve the following problem. Be sure to show all steps (V.E.S.T.) and work in order to receive full credit.

The sum of three numbers is 26. The second number is twice the first and the third number is 6 more than the second. Find the numbers.
A) A = 6, B = 12, C = 8
B) A = 5, B = 10, C = 11
C) A = 7, B = 14, C = 5
D) A = 4, B = 8, C = 14

Answer 1

The first number is 4, the second number is 8, and the third number is 14.

Step-by-step explanation:

To find the three numbers, let's assign variables to each number. Let A represent the first number, B represent the second number, and C represent the third number.

We know that the sum of these three numbers is 26, so we can write the equation A + B + C = 26.

According to the problem, the second number is twice the first, so we can write B = 2A.

The third number is 6 more than the second, so we can write C = B + 6.

Now we can substitute the values of B and C into the first equation and solve for A:

1. Substitute 2A for B: A + 2A + (2A + 6) = 26
2. Combine like terms: 5A + 6 = 26
3. Subtract 6 from both sides: 5A = 20
4. Divide both sides by 5: A = 4

Now that we know A = 4, we can substitute this value into the equations to find B and C:

1. Substitute 4 for A in B = 2A: B = 2(4) = 8
2. Substitute 8 for B in C = B + 6: C = 8 + 6 = 14

So the numbers are A = 4, B = 8, and C = 14. Therefore, the correct answer is option D) A = 4, B = 8, C = 14.