Problem 26
Question
Use the fact that page numbers on facing pages of a book are consecutive integers. The sum of the page numbers on the facing pages of a book is \(525 .\) What are the page numbers?
Step-by-Step Solution
Verified Answer
The page numbers are 262 and 263.
1Step 1: Assumptions
Let the smaller page number be represented as 'x'. Since the pages are consecutive, represent the next page number, which is a consecutive integer, as 'x+1'.
2Step 2: Setup the equation
We know the sum of the numbers on the facing pages is given to be 525. Set up an equation based on this fact. It will be: \(x + (x + 1) = 525\)
3Step 3: Solve the equation
Solve the equation for 'x'. First, simplify the left side of the equation. This gives us: \(2x + 1 = 525\). Then subtract 1 from both sides of the equation to get: \(2x = 524\). Finally, divide both sides by 2 to get: \(x = 262\).
4Step 4: Find the consecutive number
Substitute 'x' with '262' in the equation of 'x+1' to find the consecutive number. Calculating 'x+1' gives us '263'
Other exercises in this chapter
Problem 25
Solve each equation in using the multiplication property of equality. Be sure to check your proposed $$-\frac{x}{5}=-1$$
View solution Problem 25
Solve each equation. Be sure to check your proposed solution by substituting it for the variable in the original equation. $$5(2 x-8)-2=5(x-3)+3$$
View solution Problem 26
Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$t+\frac{2}{3}=-\frac{7}{6}$$
View solution Problem 26
Use the addition property of inequality to solve each inequality and graph the solution set on a number line. \(y+3 \geq 0\)
View solution