Solve the problem. See ExamplesEXAMPLE Finding Consecutive IntegersTwo pages that face eac...

Solve the problem. See Examples

EXAMPLE Finding Consecutive Integers

Two pages that face each other in this book have 269 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.

FIGURE 5 illustrates the situation.

Step 3 Write an equation. The sum of the page numbers is 269.

Step 4

Step 5 State the answer. The lesser page number is 134, and the greater page num­ber is 134 + 1 = 135. (Your book is opened to these two pages.)

Step 6 Check. The sum of 134 and 135 is 269. The answer checks.

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.

Step 1 Read the problem. We must find two consecutive odd integers.

Step 2 Assign a variable.

Step 3 Write an equation.

Step 4

Step 5 State the answer. The lesser integer is 9. The greater is 9 + 2 = 11.

Step 6 Check. When 9 is doubled, we obtain 18, which is 7 more than the greater odd integer, 11. The answer checks.

Find two consecutive even integers such that six times the lesser added to the greater gives a sum of 86.