Before mixing
Whole one, quantity x, exponential quantity a
Overall 2, quantity y, indicator quantity b (a >; b)
After mixing
Total quantity (x+y), indicator quantity c
The following relationship can be obtained:
x×a+y×b=(x+y)c
Start:
x×(a-c)=y×(c-b)
Get formula:
(A-C): (C-B) =y:x
Then we can get the unknown quantity by knowing four of X, Y, A, B and C at will. However, it is simpler to calculate c directly. When x+y is known, this method can also be used if x or y is known; It is ok to know x: y.
The related index quantity can be average value, concentration, etc. Examples are as follows:
1. Find one of the index quantities A and B..
Example 1. A container is filled with 150g of 4% salt water, and B container is filled with a certain amount of salt water. Take out 450g saline from B, put it into A and mix it into 8.2% saline. B What is the concentration of salt water in the container?
A.9.6% B.9.8% C.9.9% D. 10%
Analysis: It is known that the amount of brine taken from container B is x=450, the original amount of brine in container A is y= 150, the original concentration of brine in container A is b=4%, and the mixed concentration of brine is c=8.2%, so (a-8.2%): (8.2%-4%) =/.
Correct answer: a
Example 2. When a workshop carries out quarterly assessment, the average score of the whole workshop is 85, of which 2/3 people get more than 80 points (including 80 points), and their average score is 90 points. What is the average score below 80?
68-70 AD
Analysis: 90 10 2
Eighty-five
x 5 1
x=75
Correct answer: C.
2. find one of x and y.
Example 1. There are 40 people in the workshop, and the average score of a technical operation assessment is 80, including 83 for male workers and 78 for female workers. How many women workers are there in the workshop?
A. 16 people B. 18 people C.20 people D.24 people
Analysis: It is known that the average score of male workers is a=83, the average score of female workers is b=78, the total average score is c=80, and the total number of people in the workshop is x+y=40, then Y: X = (83-80): (80-78) = 3: 2, and the number of female workers is Y = 40× 3 ÷ (3.
Correct answer: D.
Example 2. There are a few grams of 4% brine, and the concentration becomes 10% after evaporating some water. After adding 300 grams of 4% saline, the concentration became 6.4% saline. How many grams of original salt water?
From 200 AD to 300 AD
Analysis: It is known that the original brine concentration after evaporation is a= 10%, the added brine concentration is b=4%, the weight is Y = 300g, and the mixed brine concentration is c=6.4%, so Y: X = (10%-6.4%): (6.4%-4.
Correct answer: D.
1 A city has a population of 700,000. If the urban population increases by 4% and the rural population increases by 5.4% in five years, the population of the whole city will increase by 4.8%.
What is the population of the existing towns in this city?
A30B3 1.2C40D4 1.6
Assume that the existing urban population is x million.
City X 4% 0.6%
4.8% 0.6%/0.8%=3/4, that is, X is 300,000 people.
Jia Cun 70 X 5.4% 0.8%
An experimental field used to grow ordinary rice. Now, 1/3 super rice is planted in the experimental field. When harvesting, it was found that the total rice yield in the experimental field was 1.5 times of the previous total rice yield. If the yield of ordinary rice remains the same, the ratio of the average yield of super rice to that of ordinary rice is ().
A.5:2 B、4:3 C、3: 1 D、2: 1
Assume that the average yield of super rice is x times that of ordinary rice.
Super rice X 0.5 1/3
1.5 0.5 X- 1.5 = 1/3/2/3 X = 2.5
1 X- 1.5 2/3
There are 80% more boys than girls in one class. In one exam, the average score of the whole class was 75, and the average score of girls was 20% higher than that of boys. So the average score of girls in this class is:
A.84, B. 85, C. 86 and D.87
According to statistics, there are 80% more boys than girls, so the ratio of boys to girls is 180: 100=9:5.
If the average score of boys is X, the average score of girls is 20% higher than that of boys, and the average score of girls is1.2x.
Boy X 1.2X-75 9
75 1.2X-75/75-X=9/5 X=70
Girl 1.2X 75-X
1.2X= 1.2*70=84, so the average score of girls is 84.
There are 350 cadres and workers in an organ, including 70 over 55 years old. It is now planned to carry out institutional reform, with the overall scale reduced to 1 80, and the proportion of people over 55 years old is stipulated to be reduced by 70%. What is the reduction rate of people under 55? ( )
5 1% 43% 40% d . 34%
Let the reduction ratio of people under 55 be x,
& gt55 years old 70% 17/35-X 70
170/350 17/35-X/3/ 14 = 70/280 X = 12 1/280
& lt55 years old X 3/ 14 280
12 1/280~43%
The basic price of monthly standard electricity consumption for urban residents is 0.50 yuan per kWh. If the monthly electricity consumption exceeds the standard electricity consumption, the excess will be charged at 80% of the basic electricity price. If a household consumes 84 degrees of electricity in September and pays 39.6 yuan, the monthly standard electricity consumption of the city is ().
60 degrees 65 degrees 70 degrees 75 degrees
Set the standard monthly electricity consumption x degrees.
Foundation 0.5 5/70 X
39.6/84 5/70/2/70=X/84-X X=60
Discount 0.5*80% 2/70 84-X
In a sports training center, 90% of coaches, 80% of athletes and 82% of coaches and athletes are men. The ratio of coaches to athletes is
a . 2:5 b . 1:3 c . 1:4d . 1:5
Coach 90% 2% N teaches
82% nTeaching/nTeam =2%/8%= 1:4
Team members 80% 8% nTeam
A cat eats 300 grams of food mixed with food A and food B every day. The protein content of food A is 10%, and the protein content of food B is 15%. If a cat needs 38 grams of protein every day, what is the proportion of food A?
A47%B40%C 1/3D50%
Food A 10% 7/300 is not applicable.
38/300 Na/Nb =7/300/8/300=7/8
Food B 15% 8/300 Nb
7/7+8 * 100~ 47%