Pine's forest

There were so many pines in the forest that if they were sequentially numbered 1, 2, 3,. .. , would use three times more digits than the pine trees alone. How many pine trees were there in the forest?

Result

n =  1107

Solution:

$\ \\ \ \\ 1 \cdot \ 9+2(a-9)=3a \ \\ a=-9 ... \nexists \ \\ \ \\ 1 \cdot \ 9+2(99-9)+3(b-99)=3b \ \\ \nexists b \ \\ \ \\ 1 \cdot \ 9+2(99-9)+3(999-99) + 4(n-999)=3n \ \\ n=1107 \ \\ n=1107 / 1=1107 \ \\ =1107$

Try another example

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. Cows and calves
   There are 168 cows and calves in the cowshed. Cows are in nine stalls and calves in four stalls. Same count cows are in every cow stall and three more in each calf stall than in a cow stall. What is the capacity of the stalls for cows and what for calves?
2. Basket of fruit
   In six baskets, the seller has fruit. In individual baskets, there are only apples or just pears with the following number of fruits: 5,6,12,14,23 and 29. "If I sell this basket," the salesman thinks, "then I will have just as many apples as a pear." Which
3. Apples 2
   How many apples were originally on the tree, if the first day fell one third, the second day quarter of the rest and on tree remained 45 apples?
4. Toy cars
   Pavel has a collection of toy cars. He wanted to regroup them. But in the division of three, four, six, and eight, he was always one left. Only when he formed groups of seven, he divided everyone. How many toy cars have in the collection?
5. Mom and daughter
   Mother is 39 years old. Her daughter is 15 years. For many years will mother be four times older than the daughter?
6. Mushrooms
   For five days, we have collected 410 mushrooms. Interestingly every day we have collected 10 mushrooms more than the preceding day. How many mushrooms we have collected during 4th day?
7. Walnuts
   x walnuts were in the mission. Dano took 1/4 of nuts Michael took 1/8 from the rest and John took 34 nuts. It stayed here 29 nuts. Determine the original number of nuts.
8. Cans
   How many cans must be put in the bottom row if we want 182 cans arrange in 13 rows above so that each subsequent row has always been one tin less? How many cans will be in the top row?
9. Students
   In the front row sitting three students and in every other row 11 students more than the previous row. Determine how many students are in the room when the room is 9 lines, and determine how many students are in the seventh row.
10. School year
    At the end of the school year has awarded 20% of the 250 children who attend school. Awat got 18% boys and 23% of girls. Determine how many boys and how many girls attend school.
11. Apples in baskets
    Determine how many apples are in baskets when in the first basket are 4 apples, and in any other is 29 apples more than the previous, and we have eight baskets.
12. Family
    Mom is 42 years old and her daughters 13 and 19. After how many years will mother as old as her daughter together?
13. Fifth of the number
    The fifth of the number is by 24 less than that number. What is the number?
14. AM of three numbers
    The number 2010 can be written as the sum of 3 consecutive natural numbers. Determine the arithmetic mean of these numbers.
15. Find the sum
    Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5
16. Two numbers 7
    The sum of two consecutive even numbers is 30. Find the numbers.
17. Consecutive numbers
    Sum of ten consecutive numbers is 105. Determine these numbers (write first and last).