Solve the problem. See Examples 1 and 2.EXAMPLE 1 Finding Consecutive IntegersTwo pages th...

Solve the problem. See Examples 1 and 2.

EXAMPLE 1 Finding Consecutive Integers

Two pages that face each other in this book have 225 as the sum of their page num­bers. What are the page numbers?

Step 1 Read the problem. Because the two pages face each other, they must have page numbers that are consecutive integers.

Step 2 Assign a variable.

Step 3 Write an equation. The sum of the page numbers is 225.

Step 4 Solve.

Step 5 State the answer. The lesser page number is 112, and the greater page number is 112 + 1 = 113. (Your book is opened to these two pages.)

Step 6 Check. The sum of 112 and 113 is 225. The answer is correct.

Consecutive even integers, such as 8 and 10, differ by 2. Similarly, consecutive odd integers, such as 9 and 11, also differ by 2. See FIGURE 4.

FIGURE 4

In general, if x represents an even or odd integer, x + 2 represents the next greater consecutive even or odd integer, respectively.

In this book, we list consecutive integers in increasing order.

EXAMPLE 2 Finding Consecutive Odd Integers

If the lesser of two consecutive odd integers is doubled, the result is 7 more than the greater of the two integers. Find the two integers.

Let x be the lesser integer. Since the two numbers are consecutive odd integers, then x + 2 is the greater. Now we write an equation.

The lesser integer is 9 and the greater is 9 + 2 = 11. As a check, when 9 is doubled, we get 18, which is 7 more than the greater odd integer, 11. The answers are correct.

The numbers on two consecutive checkbook checks have a sum of 357. What are the numbers?