Chapter 8 linear appliCaTionS 243- Let x = first number, x + 1 = second number, x + 2 = third number, and
x + 3 = fourth number.
Their sum is 90, so x + (x + 1) + (x + 2) + (x + 3) = 90.
xx xx
xxxx++++++=
+=
−−
===() 12 ()() 390
4690
66
484
84
4
21The first number is 21; the second, x + 1 = 21 + 1 = 22; the third, x + 2 =
21 + 2 = 23; and the fourth, x + 3 = 21 + 3 = 24.We can solve other kinds of “number sense” problems when numbers are not
consecutive. In the following problems, we will look for two numbers and will
be told their sum and how much larger one is than the other. The information
on the sum gives us the equation to solve. We use the other information to find
a relationship between the numbers so that we can represent all of the numbers
in the equation using a single variable, as we did above with consecutive
numbers.
EXAMPLE
The sum of two numbers is 70. One number is eight more than the other.
What are the numbers?
Let x = first number. (The term “first” is used because it is the first number
we are looking for; it is not necessarily the “first” in order.) The otherEXAMPLE
The sum of two numbers is 70. One number is eight more than the other.