# 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.

Correct result:

a1 =  2
a2 =  4
a3 =  8
a4 =  16

#### Solution:

$a_{2}=4 \ \\ b_{2}=4 \ \\ \ \\ s_{1}=4+4=8=2^3 \ \\ s_{2}=4 \cdot \ 4=16=2^4$
$a_{3}=8 \ \\ b_{3}=8 \ \\ \ \\ s_{1}=8+8=16=2^4 \ \\ s_{2}=8 \cdot \ 8=64=2^6$
$a_{4}=16 \ \\ b_{4}=16 \ \\ \ \\ s_{1}=16+16=32=2^5 \ \\ s_{2}=16 \cdot \ 16=256=2^8$

We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

Tips to related online calculators
Do you want to calculate least common multiple two or more numbers?
Do you want to calculate greatest common divisor two or more numbers?

## Next similar math problems:

• Two friends
Two friends met as a good man perish together for a beer. After recovery the most important topics (politics, women, football ...), one asks: - And how many do you have children? - I have 3 children. - And how many years have? Friend already not want to a
• Z9-I-4
Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Final
• Reminder and quotient
There are given numbers A = 135, B = 315. Find the smallest natural number R greater than 1 so that the proportions R:A, R:B are with the remainder 1.
• Hectares
The tractor plows the first day of 4.5ha, the second day 6.3ha and the third day 5.4ha. It worked whole hours a day, and its hourly performance did not change and was the highest of the possible. How many hectares did it plow in one hour (what is it perfo
• Endless lego set
The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. The
• The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numbers sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in
• Apples and pears
Mom divided 24 apples and 15 pears to children. Each child received the same number of apples and pears - same number as his siblings. How many apples (j=?) and pears (h=?) received each child?
• Four poplars
Four poplars are growing along the way. The distances between them are 35 m, 14 m, and 91 m. At least how many poplars need to be dropped to create the same spacing between the trees? How many meters will it be?
• Sale
If the product twice price cut by 25%, what percentage was price cut in total?
• Lesson exercising
The lesson of physical education, pupils are first divided into three groups so that each has the same number. The they redistributed, but into six groups. And again, it was the same number of children in each group. Finally they divided into nine equal g
• Tiles
How many tiles of 20 cm and 30 cm can build a square if we have a maximum 100 tiles?
• Z9–I–4 MO 2017
Numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 were prepared for a train journey with three wagons. They wanted to sit out so that three numbers were seated in each carriage and the largest of each of the three was equal to the sum of the remaining two. The conduct
• Sales of products
For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold?
• Ornamental shrubs
Children committed to plant 240 ornamental shrubs. Their commitment however exceeded by 48 shrubs. Write ratio of actually planted shrubs and commitment by lowest possible integers a/b.
• Digits A, B, C
For the various digits A, B, C is true: the square root of the BC is equal to the A and sum B+C is equal to A. Calculate A + 2B + 3C. (BC is a two-digit number, not a product).