SOLUTION: betty is thinking of two consecutive integer whose sum is 41. Let x represnt the smaller unknown integer. a. How could you represnt the larger unknown integer in terms of x?

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: betty is thinking of two consecutive integer whose sum is 41. Let x represnt the smaller unknown integer. a. How could you represnt the larger unknown integer in terms of x?      Log On


   

Question 80011: betty is thinking of two consecutive integer whose sum is 41. Let x represnt the smaller unknown integer.
a. How could you represnt the larger unknown integer in terms of x?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Since the integers are consecutive, if the smaller integer is x then the next integer
has to be one greater than x. So we can represent the two integers as x and x+1. Since
the sum of the two integers is 41 we can write:
.
x + (x + 1) = 41
.
Remove the parentheses on the left side to make the equation:
.
x + x + 1 = 41
.
Combine the two x's to get:
.2x + 1 = 41
.
Subtract 1 from both sides to eliminate the 1 on the left side. This results in:
.
2x = 40
.
Divide both sides by 2 to solve for x and the result is:
.
x = 40/2 = 20
.
Since the two integers are x and x + 1, the integers are 20 and 20 + 1 or 20 and 21.
.
If you add 20 and 21, you find that the sum of these two consecutive integers equals 41,
just as the problem required.
.
Hope this helps you to understand the problem a little better ...