Question

The sum of three consecutive numbers is 33 more than the smallest of the numbers. Find

the numbers.

Answer 1

A: The three consecutive numbers are 15, 16, 17.

Step-by-step explanation:

Let x, y, z be the numbers.

x + y + z = x + 33

y = x + 1

z = x + 2

We will solve this system of equations using the substitution method.

x + x + 1 + x + 2 = x + 33

x + x + x - x = 33 - 1 - 2

2x = 30

x = 15

y = 15 + 1 = 16

z = 15 + 2 = 17

Solving for x + y + z = x + 33:

15 + 16 + 17 = 15 + 33

48 = 48

A: 15, 16, 17.

Answer 2

15, 16 and 17

Step-by-step explanation:

Consecutive numbers mean numbers that are separated by 1 from each other. For example 5, 6 and 7 are three consecutive numbers and 5 is the smallest

Let the smallest number be x
Then the next consecutive number is x + 1
The next one after that is x + 2

Sum = x + x + 1 + x + 2 = x + x + x + 1 + 2 = 3x + 3

We are told that this sum is 33 more than the smallest number x

So 3x+3 = x + 33 Subtract x from both sides
3x - x + 3 = x + 33 -x
==> 2x + 3 = 33

Subtract 3 from both sides
==> 2x + 3 - 3 = 33 -3
==> 2x = 30
Divide both sides by 2

==> 2x/2 = 30/2
==> x = 15

So the smallest number is 15 and the three numbers are 15, 16 and 17

Verify by adding 15+16 +17 = 48
15 + 33 = 48 so consistent