1 page

1 page is torn from the book. The sum of the page numbers of all the remaining pages is 15,000. What numbers did the pages have on the page that was torn from the book?

Correct result:

x₁ =  112
x₂ =  113

Solution:

$$\begin{gathered} {\displaystyle \frac{1}{2}}\cdot n(n+1)=15000+x \\ n\cdot (n+1)=30000+2x \\ o=\sqrt{30000}=100\sqrt{3}\doteq 173.2051 \\ n\cdot (n+1)=173\cdot 174 \\ n=174 \\ x={\displaystyle \frac{1}{2}}\cdot n\cdot (n+1)-15000={\displaystyle \frac{1}{2}}\cdot 174\cdot (174+1)-15000=225 \\ x=x_1+x_2 \\ {x}_1=x\mathrm{/}2-0.5=225\mathrm{/}2-0.5=112 \end{gathered}$$

$$\begin{gathered} x_2=x_1+1=112+1=113 \\ \text{ Verifying Solution: } \\ s={\displaystyle \frac{n}{2}}\cdot (1+n)={\displaystyle \frac{174}{2}}\cdot (1+174)=15225 \\ {s}_2=s-x_1-x_2=15225-112-113=15000 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• The sum 6
  The sum of the 17 different natural numbers is 153. Determine the sum of the two largest ones.
• Sum 1-6
  Find the sum of the geometric progression 3, 15, 75,… to six terms.
• Sum of the seventeen numbers
  The sum of the 17 different natural numbers is 154. Determine the sum of the two largest ones.
• Completing square
  Solve the quadratic equation: m²=4m+20 using completing the square method
• Trapezoid 15
  Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
• Finite arithmetic sequence
  How many numbers should be inserted between the numbers 1 and 25 so that all numbers create a finite arithmetic sequence and that the sum of all members of this group is 117?
• Three members GP
  The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
• Find the sum
  Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5
• Derivative problem
  The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive and the product of one with the other power of the other is maximal.
• Sum of GP members
  Determine the sum of the GP 30, 6, 1.2, to 5 terms. What is the sum of all terms (to infinity)?
• Book
  Jitka read on holidays book that has 180 pages. In the first week read 45 pages. In the second week she read 15 pages more than the first week. How many pages left to read it yet?
• The tickets
  The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets, as well as their product, was the power of the prime number. Find all possible ticket prices.
• Sum of odd numbers
  Find the sum of all odd integers from 13 to 781.
• Substitution method
  Solve goniometric equation: sin⁴ θ - 1/cos² θ=cos² θ - 2
• Sum of four numbers
  The sum of four consecutive natural numbers is 114. Find them.
• Quarter circle
  What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
• Borrowed book
  Jane must as soon as possible return a borrowed book. She figured that when she read 15 pages a day return book in time. Then she read 18 pages a day and then return the book one day before. How many pages should have a book?