Solving the application problem of 20-way equation in sixth grade mathematics of primary school

1) The purchase price of a store 1200 yuan, with a marked price of 2,400 yuan, will make a profit of 20% when it is sold at a discount. At what discount is this product sold?

Solution: suppose the goods are discounted by X.

2400*x= 1200*( 1+20%)

2400x= 1440

X=0. Six

That's 60% off.

(2) By reducing the price by 20% to promote a certain commodity, the sales volume increased by 20%. As far as the income of this product is concerned, is this promotion successful?

Solution: Let the original price be A, the sales volume be B, and the original sales volume be AB.

The current price is (1-20%)A and the current sales volume is (1+20%)B,

Then the current sales amount is (1-20%) a * (1+20%) b = 0.8a *1.2b = 0.96ab;

At present, the sales volume of 0.96AB is less than the original sales volume of AB, so it is not successful in terms of revenue.

(3) A store sells two pieces of clothes, but for some reason, the lower purchase price leads to a loss 10 yuan, and the higher purchase price leads to a profit of at least 20%, so that there will be no loss after the two pieces of clothes are sold. What is the higher purchase price?

No loss, higher profit 10 yuan.

Solution: let the purchase price be X.

X*20%= 10

X=50

The immediate purchase price is 50 yuan.

(4) The price of a commodity delivered by a shopping mall is 6.4% lower than the original purchase price, which increases the profit by 8 percentage points. Find the original profit rate of distributing this commodity.

Solution: Let the original profit rate be X and the original purchase price be "1".

The original price is:1+x 0+x.

The current purchase price is: 1*[ 1-6]. 4%]=0。 936

[ 1+X]-0 .936=0。 936*[X+8%]

X=0 . 17

That is, the original profit rate is 17%.

1. A primary school planted 585 trees in the third, fourth and fifth grades. The number of plants in grade 4 is 65438+0.5 of that in grade 5, and the number of plants in grade 3 is 3/4 of that in grade 5. How many trees are there in grade three? 2. The number of rainy days in July is 8/ 1 1 less than that in sunny days, and the number of cloudy days is 3/22 of that in sunny days. How many rainy days are there this month? 3. Grade 5 students in a school 152 students. Boys' 65,438+0/65,438+065,438+0 were selected to take part in the math contest with five girls, and the remaining students were just equal. How many boys and girls are there in this class? There are two 44m long iron wires. If the first one is cut 1/5 and the second one is connected 2.8m, then the two lines are equal. How long are these two wires?

Answer: Grade 3 is 3/4*300=225, Grade 4 is 300* 1/5=60, and Grade 5 is 300.

If someone rides a bike from home to the train station, if they drive at the speed of15km per hour, they can arrive15min earlier than the train departure time. If he drives at 9 kilometers per hour, he will arrive 15 minutes later than the departure time. Now he plans to arrive 10 minutes earlier than the departure time. How many kilometers should he drive every hour?

Answer: The distance between the two places is:15 * [1-15/60] =11. 25 kilometers

Then arrive 10 minutes in advance, and one hour should be enough: 1 1. 25/[ 1- 10/60]= 13。 5 km

The canteen buys flour and rice, which is twice as heavy as rice. It eats/kloc-0.5 kg of rice and 20 kg of flour every day. A few days later, all the rice was eaten, leaving 80 kilograms of flour. How many Jin of rice and flour does this canteen buy?

Solution: If the rice is x Jin and the flour is 2X Jin, then the time is X/ 15 days, so there is 20*(X/ 15)+80=2X, and the solution is X= 120. So rice is 120 Jin, and flour is 240 Jin.

The following one is easier.

1:A train travels 10 hour, B train travels for 7 hours, and A train travels 276 kilometers more than B. If the two trains have the same speed, find the speed of the two trains.

Chen and Zhang ride bicycles from the same place in opposite directions at the same time. After 0.5 hours, the distance is 12.5 kilometers. Chen's speed is 12 kilometers per hour. How many kilometers is Zhang's speed? (party)

3. The number of bookcases sold by the furniture factory is one fifth of that of five X cabinets, and the number of bookcases sold is less than that of five X cabinets 120. How many bookcases and five X cabinets were sold? (party)

4. Make a rectangular iron suitcase with a capacity of 60 square decimeters. The length of the bottom is 4 decimeters, the width is 3 decimeters, and what is the height? (party)

5. The master processed 80 parts, which was less than the two companions processed by the apprentice 10. How much has the apprentice processed? (party)

6. The apprentice processed 45 parts, 5 more than half of the master. How much did the master process? (party)

Answer:

1.A X B Y

10X-7Y=267

10/X+7/Y= 1

2. Zhang x

( 12+X)*0.5= 12.5

3. Bookshelf x five cabinets y

X= one fifth *Y

X=Y- 120

4. high x

4*3*X=60

5. Apprentice X

2X- 10=80

6. main x

Half *X+5=45

1. I used a batch of cotton for the first time and used it for the second time. I used more than 300 kilograms for the second time than for the first time. How many kilograms is this batch of cotton?

Master Wang processed a batch of parts. On the first day, he processed 48 pieces, which happened to belong to these parts. The rest took eight days to finish. How many pieces are processed on average every day?

3. A book has 240 pages. If you read the whole book on the first day, the ratio of pages read on the second day to pages read on the first day is 6: 5. How many pages will you read in two days?

4. Team A needs 65,438+05 days to complete a project alone, and Team B needs 65,438+00 days. Now, in three days, Team A and Team B will finish the rest work by themselves. How many days will it take?

5. The water area is equipped with a water inlet pipe and a water outlet pipe, and the empty pool can be filled only by opening the water inlet pipe for 40 minutes; Only open the outlet pipe 1 hour to discharge all oil and water. Now open two pipes at the same time, how many hours can you fill them?

6. Make equations to solve the following problems.

(1) The original cinema had 32 rows of seats with an average of 38 people in each row. After the expansion, it will be increased to 40 rows, which can accommodate 704 more people. How many people can sit in each row after the expansion?

(2) A triangular piece of land with an area of 90 square meters has a base length of12m. What is its height?

(3) There are 78 packages in warehouses A and B, and the number of packages in warehouse A is twice that in warehouse B. How many packages are there in warehouses A and B?

(4) The distance between the two cities is 930 kilometers, and passenger and cargo vehicles leave the two cities at the same time. Six hours later, two cars met. The average speed of passenger cars is 80 kilometers per hour, and the average speed of trucks is how many kilometers per hour?

Reference answer

1.300 ÷ (-) = 4500 (kg)

This batch of cotton has 4500 kilograms.

2. (48/48)/8 = 24 (pieces)

A: On average, 24 pieces are processed every day.

3.240× = 80 (page) 80 ÷+80 = 176 (page)

Answer: I read page 176 in two days.

4.(+)×3 =( 1-)= 5 (days)

Answer; It takes five days to finish.

5. 1 ÷ (-) = 120 (minutes) 120 minutes = 2 hours.

Answer: it will be full in 2 hours.

6.( 1) solution: after expansion, assume the average number of people in each row.