Question

the sum of four consecutive integers is 2174. what are the integers? (continuation) the smallest of four consecutive integers is n. what expression represents the next larger integers? write an expression for the sum of four consecutive integers, the smallest of which is n. write an equation that states that the sum of four consecutive integers is s. solve the equation for n in terms of s. check that your answer to the previous question satisfies this equation by considering the case s= 2174.

Answer 1

Your four integers are:
x
x + 1
x + 2
x + 3

The sum of them is:
x + x + 1 + x + 2 + x + 3

So:
x + x + 1 + x + 2 + x + 3 = 2174
4x + 6 = 2174
4x + 6 - 6 = 2174 - 6
4x = 2168
4x/4 = 2168/4
x = 542

Substituting 542 for x gives you integers of 542, 543, 544 and 545.

(continuation) The smallest of four consecutive integers is n. What expression represents the next larger integers? Write an expression for the sum of four consecutive integers, the smallest of which is n. Write an equation that states that the sum of four consecutive integers is s. Solve the equation for n in terms of s. Check that your answer to the previous question satisfies this equation by considering the case s= 2174.

By using the work above, you should be able to answer the questions in the continuation.

Answer 2

The smallest of the four numbers is x.
Since the four numbers are consecutive, this means that each number is one more than the previous.
Therefore, the four numbers are:
x
x + 1
x+1 + 1 = x+2
x+2 + 1 = x+3

Now, we are given that the sum (s) of the four numbers is 2174
This means that:
s = x+x+1+x+2+x+3
s = 4x + 6

We are given that s = 2174. Substitute with s in the above equation and solve for x as follows:
2174 = 4x + 6
4x = 2174 - 6
4x = 2168
x = 2168 / 4
x = 542

Based on the above calculations, the four numbers are:
542, 543, 544 and 555