Method 1: Using remainder theorem to do:
7* 100+2*36+3*45=907
The least common multiple of 9, 5 and 4 is: 180.
907/ 180=5。 . . seven
So the three digits are:180 *1+7 =187.
180*2+7=367
180*3+7=547
180*4+7=727
180*5+7=907
* * * Yes: five.
Method 2: enumeration method:
If there are no special conditions for similar questions, the minimum value that meets the conditions is generally found by enumeration, and then the corresponding answer can be obtained by adding the least common multiple of each divisor.
Specific to this problem, we can use some special conditions to narrow the scope and reduce the number of enumerations.
① Because division by 4 is greater than 3, the number is odd;
(2) Because it is divided by 5 and is greater than 2, the number of digits is 2 or 7. According to (1), the digit should be 7;
③ Because division by 9 is greater than 7, combined with ②, the number should be at least 97; Combined with ①, after trying, the minimum value meeting the requirements is 187.
④ The least common multiple of the three divisors 9, 5 and 4 is 180, so there are five qualified three digits: 187, 367, 547, 727 and 907 * * *.
2. I bought 30 kg of oranges, 20 kg of apples, 15 kg of bananas and 18 kg of persimmons.
Buying oranges costs as much as buying apples.
The ratio of the number of oranges to apples is 3: 2.
It costs twice as much to buy persimmons as to buy bananas.
The ratio of persimmon to banana is 6: 5.
Set 3 kg of oranges, 2 kg of apples, 5 kg of bananas and 6 kg of persimmons.
3X+2X+5Y+6Y=83
6X+6X+2.4*5Y+4*6Y=228
Y=3，X= 10
I bought 30 Jin of oranges, 20 Jin of apples, 15 Jin of bananas and 18 Jin of persimmons.
36,000 yuan
5000*20%= 1000 (yuan)
1300 > 1000, indicating that the income of this person exceeds 5,000 yuan, and the tax is paid at 20%.
1300/20%=6500 yuan-the part to be taxed.
6500+800=7300 (yuan)-actual income
7300- 1300=6000 yuan-net income
4, three kinds
A
B
+
C
D
-
E
F
A
B
C
D
E
F
2
four
three
five
six
1
1
four
three
six
five
2
1
five
2
six
four
three
Namely:
24
+35
-
6 1
14
+36
-
Fifty two
15
+26
-
5,574
Because the remainder can only take 1 to 6.
You should know that the sum of any three numbers in 0-6 is not 7, but only 0, 1 and 2.
But three zeros can be divisible by seven, so there can only be two zeros.
So the * * * number is 2000/7 * 2+2 = 574.
7、 180
A bug climbs from A to B. If its speed increases by 1 meter per minute, it can arrive 15 minutes earlier. If its speed is increased by 2 meters per minute, it can arrive 15 minutes earlier. What's the distance between a and b?
Speed ratio time 1: 15
=
three
:45
Why are you doing this? Think the first time is better than the second time? 5 minutes, 45-30= 15
The ratio of speed to time is 3: 30.
Then 3+ 1=4 is the speed, and 4*45= 180.
8. Solution: Set two bottles of alcohol, A and B, with X liters and Y liters respectively. The equation is as follows:
(70%X+60%Y)/X+Y=66%
……①
(X-5)70%+(Y-5)60%/X+Y- 10 = 66.25%
……②
Solve this binary linear system of equations, x = 30l.
Y=20 liters
9. The answer should be 124365879.
Firstly, the characteristics of numbers divisible by 1 1 are described:
Count a number from right to left, add up the odd and even digits respectively, and then find their difference. If this difference is a multiple (including 0) of1,then the original number must be divisible by 1 1.
So in this question, 1-9 adds up to 45. If it is to be divisible by 1 1 and the sum of even or odd numbers is x, then X+X+ 1 1=45, and X= 17, because it is the arrangement with the smallest number. The sum of odd digits =25 is greater than 17, so the sum of odd digits =28 and the sum of even digits = 17. Because the sum of odd bits in 123456789 is less than 28, every two bits of the last six bits are exchanged into 124365879. The higher the number, the lower the better. )