Question

PLS HELP!!!!!!!!!!

Solve the given number problem. The sum of two consecutive integers is 51. What are the numbers?

A) 25 & 26

B) 26 & 27

C) 24 & 25

D) 20 & 31

Answer 1

Consecutive integers are numbers right next to each other on a number line. For example, 4 and 5, 11 and 12, 57 and 58 are pairs of consecutive integers.

To find the consecutive integers whose sum is 51, first assign a variable to one of the integers. I'll make it x.

First consecutive integer = x

The second integer is consecutive (right next to it on a number line), thus it can be represented by x + 1.

Second consecutive integer = x + 1

As stated, these two integers' sum is 51, so set their sum equal to 51, like so:

51 = x + (x + 1)

Now solve algebraically for x.

51 = x + (x + 1)

51 = x + x + 1

51 = 2x + 1

50 = 2x

25 = x

The first integer was represented by x; x = 25, thus the first consecutive integer is 25. The second consecutive integer was x + 1, or 25 + 1; the second consecutive integer is 26.

Answer:

A) 25 & 26

Answer 2

The correct answer is A) 25 and 26.

In my opinion, the easiest way to solve this problem is by process of elimination and guess and check.

First, we should eliminate option D because these are not consecutive integers (meaning that they are two numbers that are one after the other). We can also eliminate options B and C because 26+27 and 24+25 are over and under the value of 51, respectively. This leaves only option A, which works because 25 and 26 are consecutive integers and 25+26=51.

Hope this helps!