2 math problems in 6th grade are solved with proportions

1. (1) Assigned to x masters, then apprentices x-100x-100):(x-100-75)=x:(x-100)x-100) =(x-175)x

x²-200x+100×100=x²-175x25x=100×100

x=400 is allocated to 400 masters, then 300 apprentices.

2) If the master completes X, the apprentice completes X-75

x：(x-75)=(x+1000）：x

x²=x²-75x+100x-75×10025x=75×100

x=300 is allocated to the master, 300 + 100=400, so if it is allocated to the master, 400 are assigned to the master, then there are 300 apprentices.

2. Sister and brother go to school in the same school, 1200 meters from home to school, every morning, the younger brother walks 5 minutes before the sister, but arrives at school 3 minutes earlier than the sister, the speed ratio of the sister and brother is 6:5, what is the speed of the sister and brother?

Solution: If the sister takes x, then the younger brother takes x+(5-3)=x+2 The speed ratio of the two sisters and brothers is inversely proportional to the time.

x：（x+2)=5：6

6x=5x+10

x=10 The sister takes 10 minutes, then the younger brother takes 12 minutes.

Sister's speed 1200 10 = 12 meters min.

The speed of the younger brother is 1200 12 = 10 meters min.

This question does not tell the distance, it cannot be calculated)

1.Solution: Let the task be x The speed of the master and the speed of the apprentice are a fixed value of the master to do x apprentices to do x-75 apprentices to do x master to do x+100 then the equation x:

x-75） = （x+100） ：xx^2=x^2+25x- 7500

x = 300 (same number of parts).

2. Did you write the title correctly? The younger brother walked for 5 minutes first, and arrived 3 minutes earlier than his sister, which is 2 minutes longer than his sister, and there is a lack of a condition.

There is a problem with the second question. The younger brother takes more time than the elder sister, and the speed is faster than the elder sister, so he must have walked more distances.

Solution: The number of pencils and pens purchased in stationery stores is 4x and 3x, according to the title:

4/5（4x-10）=3x

x=40 The number of pencils and pens purchased at stationery stores is 160 and 120.

A total of 7x pens were purchased at the stationery store, 4x pencils and 3x pens.

4/5（4x-10）= 3x

then x = 40, 4x = 160, 3x = 120 so 160 pencils and 120 pens.

1/10 ……Team B efficiency.

Set Team A's efficiency to x

2(x+1/10):1=1:3

6x+3/5=1

6x=2/5

x=1/15

A: It can be completed in 15 days.

1/10 2 1/5

1/3 1/5 2/15

2/15 2 1/15

1 1/15 15 days.

If teams A and B work together for 2 days, they can complete 1 3 of this project, and two people together can complete 1 6 per day

If team B can complete all the work in 10 days alone, B's work efficiency is 1 101 6-1 10 = 1 15

The ergonomics of B is 1 10, and the sum of ergonomics is 1 3 2=1 6, then the ergonomics of A is 1 6-1 10=1 15, so A alone needs 1 1 15=15 days.

There are two scenarios. 1. It can be done in 10 days when two people work at the same speed. Second, it is difficult to answer when the two are different. One less known condition for this question is what the ability of the two people to work is.

A and B two teams can complete 1 3 in two days, then 2 divided by 1 3 equals 6 is the time required by A and B to work together, then 1 divided by 6 equals 1 6 is the work efficiency of A and B. Team B works alone, if it is completed in ten days, 1 divided by 10 is equal to 1 10 is the ergonomics of B, the total ergonomics minus the ergonomics of B is the ergonomics of A, and the ergonomics of B is divided by 1 to be B's working time.

If you want to use the proportional solution, you know that the work efficiency multiplied by the working time equals the total amount of work, and the total work can be seen as 1 first, that is:

Solution: This project can be completed by doing it alone for x days.

1/3÷2-1/10)x=1

1÷（1/3÷2-1/10）

15 (days) A and B teams can complete 1 3 of this project in 2 days, then two people can complete 1 6 per day, and B team can complete all the projects in 10 days alone, and the efficiency is 1 10, and then use the 1 6 that two people can complete every day minus 1 10 that team B does every day, and what comes out is that team A does 1 15 per day, then, the total workload"1"Team A asked for 1 15 a day.

Hello, the ergonomics of B is 1 10, and the ergonomics sum is 1 3 2=1 6, then the ergonomics of A is 1 6-1 10=1 15, so A alone needs 1 1 15=15 days. This is an engineering problem that does not need to be solved in proportions.

This problem should grasp the total amount of work, that is, A's work efficiency multiplied by its working time is equal to unit 1, and A's work efficiency is equal to the efficiency of two teams and minus the efficiency of team B. Therefore, this problem can be solved in this way: if a team can complete this project in x days alone, then.

1/3÷2-1/10)x=1 x=15

Regard the whole project as 1, A and B two teams work together to complete the whole project in 2 days 1 3, then one day to complete: 1 3 2 = 1 6, team A alone to complete the whole project in 10 days, then the amount of one day to complete the whole project: 1 10 = 1 10, by A and B two teams together to complete the whole project 1 3, let B work efficiency a, then (1 10 a) 2 = 1 3, the solution a = 1 15, then B alone to complete the project time:

1.Set to x km: (1 4x+50): x=1:3, x=600

2.Set the required time to x:

2：40%=x：1 x=54.Solution: This batch of parts can be produced in actual x days.

576：3=(160x12)：x

x=103 108:(4+5)=108:(5-4) 9 is 12 people less.

Solution: A and B are x kilometers apart.

1/4x+50=1/3x

50=1/12xx=600

1 20% = 5 (hours).

5-2=3 (hours).

.Solution: Let the two places of A and B be separated by x kilometers.

1/4x+50):x=1/3

x=600 solution: Let this car take x hours to get from place A to place B.

40%;2=1;x

x=5 solution: This batch of parts can be produced in actual x days.

576;3=(160x12);x

x=10

50 divided by 1 3-1 4 = 600 km2 divided by 40% = 5 hours 108 divided by 5 plus 4 and multiplied by 5-4 = 9 people 160 12 (576 3) = 10 people.

1) Solution: Let x basin be required, 2:x=:12

x=16A: 16 pots are needed.

2) Solution: Set to take x hours.

50：（1+20%）*50=x：12

60x=600

x=10A: It takes 10 hours.

It will take x hours to set up the whole train journey.

x:1=:7/9

7x 9=x=hours.

It's a matter of proportion.

If the remaining journey takes x hours, there is.

x：2/9=：7/9

x = hours.

If the remaining journey takes x hours, there is.

x：2/9=：7/9

x = hours.

Use the method of solving equations:

Solution: Let the younger brother go to the number of the xth tree.

84：36=(22-1)：(x-1)

84(x-1）=36*21

x=10A: When the elder brother walks to the 22nd tree, the younger brother walks to the 10th tree.

Method 2: 36 84 (22-1)=36 84 21=36 21 84=9,9+1=10

Note: The reason why 22-1 is used is because when my brother walked to the 22nd tree, he only walked 21 trees.

What is the distance between the willow trees.

Let the younger brother walk to the xth tree, then.

22×84=36x

So x=22 84 36=

The distance that older brother walks per minute is proportional to the distance that older brother walks to 22 trees is 21 tree distance.

84 36=21 x x=9 So the younger brother walked to the 10th tree.