Chapter 8 linear appliCaTionS 241
Number Sense
Many problems require us to use “common sense” to solve them—that is, basic
mathematical reasoning. For instance, when a problem refers to consecutive
integers, we are expected to realize that any two consecutive integers differ by
one. If two numbers are consecutive, we normally let x equal the first number
and x + 1, the second.
EXAMPLE
The sum of two consecutive integers is 25. What are the numbers?
Let x = first number, and x + 1 = second number.
Their sum is 25, so x + (x + 1) = 25.
xx
x
x
x
x
++=
+=
−−
=
=
=
() 125
2125
11
224
24
2
12
The first number is 12 and the second number is x+ 1 = 12 + 1 = 13.
The sum of three consecutive integers is 27. What are the numbers?
Let x = first number, x+ 1 = second number, and x+ 2 = third number.
Their sum is 27, so x + (x + 1) + (x + 2) = 27.
xx x
x
x
x
x
++++=
+=
−−
=
=
=
() 12 () 27
3327
33
324
24
3
8
The first number is 8; the second is x + 1 = 8 + 1 = 9; the third is x + 2 =
8 + 2 = 10.
EXAMPLE
The sum of two consecutive integers is 25. What are the numbers?
