# 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 =  25
x2 =  26

#### Solution:

$\dfrac{ 1 }{ 2 } \cdot \ n(n-1)=15000 + x \ \\ n \cdot \ (n-1)=30000 + x \ \\ \ \\ o=\sqrt{ 30000 }=100 \ \sqrt{ 3 } \doteq 173.2051 \ \\ \ \\ n \cdot \ (n-1)=173 \cdot \ 174 \ \\ \ \\ n=174 \ \\ \ \\ x=\dfrac{ 1 }{ 2 } \cdot \ n \cdot \ (n-1)-15000=\dfrac{ 1 }{ 2 } \cdot \ 174 \cdot \ (174-1)-15000=51 \ \\ x=x_{1}+x_{2} \ \\ \ \\ x_{1}=x/2-0.5=51/2-0.5=25$
$x_{2}=x_{1}+1=25+1=26$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:

Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Do you want to round the number?

## Next similar math problems:

• Coils of transformer
The primary coil of the transformer has 400 turns, a current of 1.5 A passes through it and is connected to a voltage of 220 V. For the secondary coil, find the voltage, current, and a number of turns if the transformation ratio k = 0.1.
• Lookout tower
How high is the lookout tower? If each step was 3 cm lower, there would be 60 more of them on the lookout tower. If it was 3 cm higher again, it would be 40 less than it is now.
• Coils of transformer
The primary coil of the transformer has 1100 turns and is connected to a voltage of 220V. How many turns does the secondary coil have when the voltage on it is 55 V? Determine the transformation ratio and decide what kind of transformation is it.
• Sailboat
The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck.
• Square and circles
The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a.
• Cylinder container
The cylindrical container with a diameter of 1.8 m contains 2,000 liters of water. How high does the water reach?
• Chord of triangle
If the whole chord of the triangle is 14.4 cm long, how do you calculate the shorter and longer part?
• Hexagonal pyramid
Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.
• On a line
On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].
• Shell area cy
The cylinder has a shell content of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder.
• The cylinder
The cylinder has a surface area of 300 square meters, while the height of the cylinder is 12 m. Calculate the volume of this cylinder.
• Pentadecagon
Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
• In the
In the rectangle ABCD, the distance of its center from the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents of the rectangle. Express the result in cm2.
• Dodecagon
Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
• Twice of radius
How many times does the surface of a sphere decrease if we reduce its radius twice?
• An observer
An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
• Trip with compass
During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip?