The application problem of the ratio of Olympic numbers 1 knowledge points
The concept of 1. number of copies
A: B = A: B, which can be regarded as A and B, and the number of copies can be added or subtracted, such as the sum of A and B is
A+b, A has more a-b than B.
2. Corresponding quantity and share
If the corresponding quantity of A is X, then the corresponding quantity of 1 is X÷a. ..
And if the corresponding quantity of 1 is x, then the corresponding quantity of a is x× a.
3. Uniform ratio (chemical connection ratio)
In the two ratios, 1 may represent different amounts. For example, A: B = 2: 3, B: C = 2: 5, where B comes first.
The proportion on the surface represents 3 copies, and the proportion on the back represents 2 copies. The least common multiple of 3 and 2 should be 6, and the two ratios should be separated.
For A: B = 4: 6 and B: C = 6: 15, the two ratios are unified and can be written as A: B: C = 4: 6: 15.
Example:
(1) The ratio of Eddie to Dayuan is 4: 5. Eddie has 20 pieces of candy, so there is one piece of candy in the big width.
(2) Eddie and Dakuanyi * * * have 45 pieces of sugar, and their sugar ratio is 4: 5, so Eddie has a piece of sugar and Dakuanyi has a piece of sugar.
(3) Eddie, Dakuan, and Weier have 45 pieces of sugar, and the ratio of sugar among them is 4: 5: 6, so Eddie has it.
A piece of candy, Dakuan takes a piece of candy, Wei Er takes a piece of candy.
(4) The ratio of sugar number among Eddie, Dawuan and Will is 4: 5: 6, and knowing that wilby Aidido 10 sugar, then three.
People have a piece of candy.
analyse
(1) Eddie 4 is 20 pieces, so 1 is 20÷4=5 pieces, and the width is 5 pieces, so the width is 5×5=25 pieces;
(2) Eddie has 4 parts, and the width is 5 parts, totaling ***9 parts, corresponding to 45 pieces of sugar, so 1 part is 45÷9=5 pieces of sugar.
Eddie has 5×4=20 pieces of sugar, and its width is 5×5=25 pieces.
(3) A * * * has 4+5+6= 15, corresponding to 45 pieces of sugar, so 1 is 45÷ 15=3 pieces of sugar, so Aidi has 3×4= 12 pieces of sugar with a width of 3.
(4) Weil has 6-4=2 portions more than Eddie, corresponding to 10 portion of sugar, so 1 0 ÷ 2 = 5 portions of sugar and 4+5+6 = 15 portions for three people, so * * has it.
1, in order to prevent colds, people often decoct ginger and brown sugar with water, generally according to the mass ratio of 1: 2: 50. Beibei caught a cold, and her mother gave him 2 12 grams of ginger soup at a time. So how many grams of ginger and brown sugar do you need to prepare? (The water loss during boiling can be ignored)
2.( 1) The ratio of money between Eddie and Vera is 3: 2. After mom gave Eddie 4 yuan more money, the ratio of money on Eddie and Vera was 8: 5. How much money does Vera have?
(2) The original card ratio of Eddie and Will is 8: 7. If Eddie gives Will four cards, the ratio between them becomes 18: 17. How many cards does Eddie have?
(3) The ratio of extracurricular books between Eddie and Vera's family is 5: 4. After Dakuan asked Eddie and Vera to borrow five extra-curricular books each, the ratio of extra-curricular books between Eddie and Vera became 9: 7, so how many extra-curricular books did Eddie and Vera each have?
3. The original money ratio between Party A and Party B was 6: 5. Later, Party A got 180 yuan and Party B got 30 yuan. At this time, the currency ratio of Party A and Party B is 18: 1 1. What was the original sum of money?
The application problem of the Austrian number ratio is 2 1. In 3: 5, if the former item is added with 6, how much should the latter item be added to keep the proportion unchanged?
On the diagram of 2. 12: 1, the length of the precision part is 6 cm, so what is its actual length?
Xiaoming, Xiaoqing and Xiaohua make red flowers. Xiaoming spends more flowers than Xiaoqing 16. The ratio of flowers made by Xiaoqing in Kobanawa is 5: 6. The ratio of the total number of flowers made by Xiaoqing and Xiaohua to that made by Xiaoming is 1 1: 8. How many flowers did Xiaoming make?
4. A math contest was held in grade five, with class one accounting for 1/3 of the total number of participants. The ratio of the number of participants in Class Two to Class Three is 1 1: 13, and Class Two is 8 fewer than Class Three. How many people are there in Class Three?
5. Buy A and B pencils * * 2 10. Each pencil is worth 3 yuan, and each pencil is worth 4 yuan. The price of two pencils is the same. How many pencils?
6. Natural numbers A and B satisfy1/a-1/b =1182, and A: B = 7: 13, so how much does A+B get?
7. There are three grades in bright primary school. The number of senior one students accounts for 25% of the total number of students in the school. The ratio of students in grade two and grade three is 3: 4. It is understood that there are 40 fewer senior one students than senior three students. How many students are there in Grade One?
8. The walking speed ratio of Party A and Party B is 13: 1 1. If Party A and Party B leave from A and B at the same time and meet face to face, they will meet in 05 hours. If they go in the same direction, how many hours will it take to catch up with Party B?
9. The ratio of chickens, ducks and geese is 3: 2: 1. Draw a fan-shaped statistical chart. What is the central angle of the sector representing the number of chickens?
10. Given that the ratio of A to B is 5: 3 and the sum of their greatest common divisor and least common multiple is 1040, what is the number of A?
The application problem of the Olympic proportion is 3 1. Girls account for 5 1% of the total number of students in a school. If there are 735 boys in this school, how many girls are there in this school?
2. If 3a = 4b and 5b = 6c, how many times is A greater than C?
3, a supermarket to carry out promotional activities, the original 10% off sales of eggs to 20% off sales. In this way, you can spend less 1.75 yuan by buying 5 Jin of eggs at a time. So how much is the original price of eggs a catty?
4. The price of a commodity is 25 yuan/piece, so a 20% discount is required, and the price will be reduced after 2 yuan.
5. The purchase price of goods is one yuan/piece, and the price of goods in the peak season of sales is 50% higher than the purchase price; After the peak sales season, the products are promoted at a price of 30%. At this time, the price of a product is ().
(a) 1.5a(b)0.7a(c) 1.2a(d) 1.05 a
6. Bend a 24 cm long iron wire into a rectangle, length: width = 5: 1, and find the area of this rectangle.
7. A traditional Chinese medicine contains four components: A, B, C and D. The weight ratio of these four components is 0.7: 1: 2: 4.7. Now, how many grams of these four herbs do you need to prepare 2100g of this Chinese medicine?
8. Draw * line oc with right angle ∠aob. If ∠aoc:∠boc=3:2, find the degree of ∠boc.
9. The ages of Party A, Party B and Party C are related as follows: Party A is twice as old as Party B and Party C is 10 times, while last year, Party B was six times as old as *. Ask three people their ages?
10, the class committee decided that Dabao and Bauer would be responsible for buying 22 ballpoint pens and pens and giving them to the students in the paired mountain schools. They went to the mall and saw each 2 yuan for ballpoint pens and each 6 yuan for pens. If you buy a 10% discount ballpoint pen and a 20% discount pen, please write a purchase plan on the premise that the required cost does not exceed that of 60 yuan.
Four examples of the application of the ratio of Olympic number 1
A workshop has to process 2220 parts, and one person does it. The working time ratio required by Party A, Party B and Party C is 4∶5∶6. Now it is handled by three people * * *, and it is required to complete the task. How much has each of the three people handled?
The working time ratio required by Party A, Party B and Party C alone is 4∶5∶6, and the working efficiency ratio of Party A, Party B and Party C is 6∶5∶4, which is solved by the idea of proportional distribution.
The mistake in commenting on the above answer is that the work efficiency ratio of A, B and C is 6∶5∶4. It is true that if the working time ratio of Party A and Party B is 4∶5, then the working efficiency ratio of Party A and Party B is 5∶4, which is correct. However, if the working hours of Party A, Party B and Party C are converted from 4: 5: 6 to the working efficiency of Party A, Party B and Party C from 6: 5: 4, it would be a big mistake! Yes, the ratio of work efficiency is equal to the inverse ratio of working hours. From the known situation, the working time ratio of Party A and Party B is 4∶5, so the working efficiency ratio of Party A and Party B is 5∶4. The working time ratio of Party B and Party C is 5: 6, so the working efficiency ratio of Party B and Party C is 6: 5. Here, "5: 4" refers to Party A's 5 copies and Party B's 4 copies, and "6: 5" refers to Party B's 6 copies and Party C's 5 copies, all of which are double comparisons, which also means that the number of "Party B" in the first two proportions is different. How to directly convert these two ratios into a continuous ratio of work efficiency of Party A, Party B and Party C? Obviously, it is wrong to regard the working efficiency of Party A, Party B and Party C as 6∶5∶4 in the above solution.
It is easy to see that, because 5: 4 = 15: 12, 6: 5 = 12: 10, the efficiency ratio of Party A and Party B is 5: 4, and that of Party B and Party C is 6: 5.
Example 2
There are two bottles of salt water of the same weight. The ratio of salt and water in bottle A is 1: 8, and that in bottle B is 1: 5. Now put two bottles of salt water together. What is the weight ratio of salt to water in mixed brine?
It is misunderstood that the weight of salt in bottle A is "1" and the weight of water is "8", while the weight of salt in bottle B is "1" and the weight of water is "5". Therefore, when two bottles of brine are combined, the weight of salt is (1+65433).
( 1+ 1)∶(8+5)=2∶ 13
A: The weight ratio of salt to water in mixed brine is 2: 13.
The main mistake in evaluating the above solutions is to regard the simplest ratio of the weight of two substances as the ratio of the specific gravity of two substances. The weight ratio of salt and water in bottle A is 1: 8, which does not mean that the weight of salt in this bottle of brine is 1 kg, and the weight of water is 8 kg, and so is bottle B. From the known conditions, it can be seen that there are 1 part salt, 8 parts water, 9 parts salt and water (1+8. The above solution is simply to add the parts with different weights of salt and water in two bottles of brine, and then combine the two "sums" to form a ratio, and the wrong solution is obtained.
The correct answer is:1∶ 8 = 2 ∶16,2+16 =18;
1∶5=3: 15,3+ 15= 10。 (2+3)∶( 16+ 15)=5:3 1
A: The weight ratio of salt to water in mixed brine is 5: 3 1.