FREQUENTLY ASKED QUESTIONS
The age difference between two people is constant.
(2) The age of two people is increasing or decreasing at the same time.
(3) The multiples of two people's ages are changing.
Three basic characteristics
The age difference between two people is constant.
(2) The age of two people is increasing or decreasing at the same time.
(3) The multiples of two people's ages are changing.
Solution formula
The precession will not change, when adding and subtracting.
With the change of age, the multiple is also changing.
Grasp these three points and everything will be easy.
Example 1: Xiaojun is 8 years old and his father is 34 years old. A few years later, his father was three times older than Xiaojun. The precession will not change, this year's age is almost 34-8=26, and it will not change in a few years. Knowing the difference and multiple, it becomes the problem of difference ratio. 26÷(3- 1)= 13. A few years later, the age of dad was 13×3=39, and the age of Xiaojun was 13× 1= 13.
Ideas and methods to solve problems
1. can be used to solve the "differential multiple problems" ideas and methods.
Example 1: Dad is 35 years old and Liangliang is 5 years old. How old is dad this year? What about next year?
Solution: 35 ÷ 5 = 7 (times)
(35+ 1) ÷ (5+ 1) = 6 (times)
My father is seven times as old as Liang Liang this year.
Dad will be six times as old as Liang Liang next year.
Example 2: Mother is 37 years old and daughter is 7 years old. In a few years, my mother will be four times as old as my daughter.
Solution: (1) How old is the mother than the daughter? 37-7 = 30 years old
(2) A few years later, the mother is four times as old as her daughter? 30(4- 1)-7 = 3 (year)
Column into a comprehensive formula (37-7) ÷ (4- 1)-7 = 3 (year).
A: After three years, the mother is four times as old as her daughter.
Example 3: A said to B, "My age is your present age, and you were only 4 years old". B said to A, "When my age is your present age in the future, you will be 6 1 year old". What are the ages of Party A and Party B now?
Solution: This involves three years: one year in the past, one year this year and one year in the future.
List analysis:
Last year, this year, the next year.
A □ Age△ Age 6 1 year
B 4 years old □ years old △ years old
Two □ in the table represent the same number, and two △ represent the same number.
Because the age difference between two people is always equal: □-4 = △-□ = 6 1-△, that is, 4 □, △, 6 1 becomes arithmetic progression, so 6 1 should be three years older than 4.
So the age difference between them is: (6 1-4) ÷ 3 = 19 (years old).
A The age this year is △ = 6 1- 19 = 42 (years old).
B The age this year is □ = 42- 19 = 23 (years old).
A: A is 42 years old and B is 23 years old.
2. The most basic questions of age are yesterday and today, one is the proportional method, and the other is the table equation method.
Solve the age problem by proportional method;
Example 1: A year ago, the combined age of parents was seven times that of the two brothers. Four years later, the combined age of parents is four times that of the two brothers. It is understood that my father is two years older than my mother. How old is mother this year?
Analysis:
1) The age problem can be solved by the equation method, but for this multiple problem, the proportional method is the best, fastest and simplest method.
2) The key to solving problems by the proportional method is to find invariants, and the invariants of the age problem are the age difference.
3) This question is about the age gap between parents. If we know the age gap between parents, the problem will be solved.
4) for the convenience of writing, the sum of parents' ages is represented by a, and the sum of brothers' ages is represented by b.
5) A year ago: a:b=7: 1, age difference 7-1= 6;
Four years later, that is, five years later: a:b=4: 1, and the age difference is 4-1= 3;
If the age difference is fixed, it is necessary to unify the age difference after four years into six parts, a: b = 4: 1 = 8: 2,
Age difference =8-2=6 copies;
A year ago, the sum of parents' ages was 7(7: 1), and five years later, the sum of parents' ages became 8 (2 out of 8: 8).
And the parents' age has increased by 5×2= 10, then each =(8-7)× 10= 10;
The sum of parents' ages after four years = 10×8=80 years old; This year's age and =80-4×2=72 years old;
The sum of ages =72, and the age difference between parents =2, then the mother's age =(72-2)/2=35.
Solve the age problem by table equation method;
Example 2: Big-headed dad said to his little-headed son, You were only 4 years old when I was your age. The little son said to the big father, when my age reaches your present age, you will be 67 years old. How old are father and son now?
Analysis: It is no longer convenient to use the proportional method for this kind of questions, but it is still necessary to use the basic conditions of constant age difference:
Draw a table first.
2) You can assume that your son is now X years old.
3) Fill in the first column of the form according to the first condition and get the age difference.
4) At this point, according to the age difference, you can fill in the father's age:
5) Fill in the third column according to the second condition:
6) At this time, the age difference between father and son in the third column should also be equal to x-4, and the equation can be listed:
67-(2x 4)= x-4
X=25
So dad's age now =2×25-4=46 years old.
practice
1. Teacher Liang asked Teacher Chen how many children she had, and she said, "Now my lover and I are six times older than children; Two years ago, our total age was 10 times that of our children; Six years later, our total age is three times that of our children. " Ask teacher Chen how many children she has.
Analysis: Now my lover and I are six times as old as children, that is, more than five times; Two years ago, the total age of our children was 10 times, that is, more than 9 times; Six years later, our age will be three times that of our children, that is, twice. If it is two children, 5×9×2=90, which is obviously unreasonable. If there are three, the sum of the children's present ages is regarded as one, so each = (18× 3-12)/3 = 14, that is, the children's present ages and14, and the parents' present ages and 6× 14=84.
Therefore, Mr. Chen has three children.
Xu Peng is 30 years younger than his father this year. Four years later, my father was three times as old as Xu Peng. How old are Xu Peng and his father this year?
Analysis: Four years later, my father's age is three times that of Xu Peng, that is, my father's age is twice that of Xu Peng (3- 1 = 2 times), which is exactly the age difference between them (30 years old). So four years later, Xu Peng's age should be:
30÷ (3-L) = 15 (years old);
Xu Peng's age this year is: 15-4 = 1 1 (years old);
Dad's age this year is: 1 1+30 = 4 1 (years old).
The age of a family of four is 100 years old. My brother is 8 years older than my sister and my father is 2 years older than my mother. 10 years ago, their family was 65 years old. Think about it. How old are you this year?
Analysis: The total age of four people in the family this year is 100, so the total age of the family ten years ago should be reduced by 10× 4 = 40; But 100-65 = 35, which means there was no younger brother ten years ago. The gap of 5 is the younger brother's age. 100 MINUS the age of sister and brother is the age of parents and children. So this year's younger brother: 10× 4-( 100-65) = 5 (years old);
Sister this year: 5+8 = 13 (years old);
Father this year: (100-5- 13+2) ÷ 2 = 42 (years old);
Mother this year; 42-2 = 40 (year).
One day, Teacher Song said to Xiao Fang, "When I was your age, you were only 1 year old." Xiao Fang said, "When I grow up to your age, you will be 43 years old." How old are they now?
Analysis: Xiao Fang's age from 1 to present age, from present age to teacher Song's present age, and from teacher Song's present age to 43 are equal, just equal to the age difference between them, so the age difference between teacher Song and Xiao Fang is (43- 1) ÷ 3 = 14 (years old). It can be known that Xiao Fang's present age is 1+ 14 = 15 (years old), and Teacher Song's present age is 15+ 14 = 29 (years old).
When asked about others' age, he said, "I will be 22 years old the day after tomorrow, and I was less than 20 years old on New Year's Day last year." Is such a thing possible?
Analysis: This is possible. This person's birthday is 1 2nd of the month. When he spoke, it was 65438+February 3 1 this year. That's it. He was 19 years old on New Year's Day last year, and he was 65438+20 years old on 1 2 October this year. He is still 20 years old on 1 2 February, and he will be 22 years old on 1 2 February next year.
6. There is a family where three grandparents happen to live under the same roof. On this day, their ages add up to exactly 100 years old. I also know that grandpa's age is exactly equal to the number of months of his grandson, and the number of weeks of his father is exactly equal to the number of days of his son. Please calculate the ages of grandparents and grandchildren.
Analysis: As long as we understand the relationship among age, month, week and days, we can find clues to solve this problem.
Grandpa's age is exactly equal to the number of months spent by his grandson, with 12 months in a year, so his age is 12 times that of his grandson. The number of weeks spent by the father is exactly equal to the number of days spent by the son, so the father is seven times older than the son.
Therefore, if the grandson's age is 1, then the father accounts for 7 and the grandfather accounts for 12. So we can get: the age of grandson:100 ÷ (1+7+12) =100 ÷ 20 = 5 (year); Father's age: 5× 7 = 35 (years); Grandpa's age: 5× 12 = 60 (years old).