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.

When the lesser of two consecutive integers is added to three times the greater, the result is 43. Find the integers.