Math problems, the master is coming... With a system of binary linear equations...

Set the flat road x, uphill y, downhill 142-x-y

Column equations: x 30 + y 28 + (142-x-y) 35 = x 30 + y 35 + (142-x-y) 28 = x = 30, y = 42, 142-x-y = 70 When you go, the flat road is 30 km, the uphill is 42 km, and the downhill is 70 km.

Uphill x downhill y flat road 142-x-y back downhill x uphill y zeping road 142-x-y142-x-y) 30+x 28+y 35=142-x-y) 30+x 35+y 28=Solve the result.

Solution: Set uphill x, downhill y, flat road 142-x-y

4 hours 30 minutes = hours, 4 hours 42 minutes = hours.

Make use of the equation of time:

142-x-y) 30+x 28+y 35=142-x-y) 30+y 28+x 35=x=x=42,y=70, then the flat road has: 142-70-42=30 km.

Set uphill x km, flat road y km, downhill z km, x+y+z=142x 28+y 30+z 35=

z/28+y/30+x/35=

As a result, you can count it yourself, and you don't want to forget it.

Set uphill x, downhill y, flat road 142-x-y.

142-x-y) 30+x 28+y 35=142-x-y) 30+x 35+y 28=4+42 60 The solution is x= , y= .

Set roosters, hens, and chicks are x, y, and z respectively, and they are calculated by the title

x＋y＋z＝100

5x＋3y＋(1/3)z＝100

There are two equations, three unknowns, called indefinite equations, with multiple solutions.

Order 3: 7x 4y 100;

So y=(100-7x) 4=25-2x+x 4 let x 4=t, (t is an integer) so x=4t

Substituting x=4t into 7x+4y=100 obtains: y=25-7t, easy to get z=-75-3t

So: x=4t

y=25-7t

z=75+3t

Because x, y, Jian Hui z is greater than or equal to 0

Therefore, 4t is greater than 0

25-7t is greater than or equal to 0

75+3t is greater than or equal to 0

The solution is that t is greater than or equal to 0 less than or equal to 25 7, and because t is an integer.

So t = 0, 1, 2, 3 (here don't forget that t is possible to be equal to 0) when t = 0.

x=0，y=25，z=75

When t=1.

x＝4；y＝18；z＝78

When t=2.

x＝8；y＝11；z＝81

When t=3.

x＝12；y＝4；z＝84

1.Saving time is, of course, the cooperation of A and B.

2.The weekly decoration cost of A and B is X y

x+y)*6=

x*4+y*9=

The solution is x=2 3 y=4 15

To save money, it can already be seen on the topic that the decoration cost is < that is, A does B first, and then does it, so there should be no need to calculate the weekly cost of A and B.

Let's do the math for you.

If company A needs x yuan for a week to decorate, and company B needs y yuan for a week to decorate, 6 (x+y) = 52000 from the title

4x+9y=48000

The solution is x=6000, y=the exact value is 8000 3, rounded to one digit for easy comparison of size).

Therefore, if you think about it from the perspective of saving time, you should choose Company A, and if you think about it from the perspective of saving money, you should choose Company B.

ps: If A and B work together, it is not as fast as Company A, and the two upstairs did not understand the title = . =）

1) Let A complete x every week and B complete y every week

Simultaneous equations: 6x + 6y = 1——— 4x + 9y = 1———

The solution yields x= 1 10 , y= 1 15

That is, it takes 10 weeks for A to complete alone, and 15 weeks for B to complete alone, so Company A should be selected from the perspective of saving time.

2) Set A to charge a million yuan per week, and B to charge B million yuan a week.

Simultaneous equations: 6a + 6b =

4a + 9b =

The solution is a = 6 100,000 yuan and b = 4 150,000 yuan multiplied by the time required for each.

A: 6 10 10 = 60,000 yuan.

B: 4 15 15 = 40,000 yuan.

Therefore, from the perspective of cost saving, company B should be chosen.

(1) Cooperation between A and B.

2) A and B cooperation.

Set up the vertical car x production screws by the title, and y production nuts.

x+y=28

2*12x=18y (where 12x is the total number of screws produced, 18y is the total number of screw round dies produced, and the two are multiples of the cavity).

The solution is x=12 and y=16

A pedestrian street is equipped with a number of bonsai in three shapes: A, B and C. A bonsai is made up of 15 red flowers, 24 yellow flowers, and 25 purple flowers. The second bonsai is composed of 10 red flowers and 12 yellow flowers.

The C bonsai is made up of 10 red flowers, 18 yellow flowers and 25 purple flowers. These bonsai have a total of 2,900 red flowers, 3,750 purple flowers, and how many yellow flowers are shared?

solution, let A have x basin B y basin , get:

Since purple flowers are only available in A and C, and 3750 flowers are used, then the number of pots of C is (3750-25x) 25, which is 150-x

2,900 safflowers were used.

So 15x+10y+10(150-x)=2900, simplified 5x+10y=1400, simplified x+2y=280, Huanghuayi shared 24x+12y+18(150-x), simplified, 6x+12y+2700

It is known that x+2y=280 then 6x+12y=6(x+2y)=1680, so the yellow flower 6x+12y+2700=1680+2700=4380*** solution, let A x, B y, C z, get:

15x+10y+10z=2900

25x+25z=3750

From the above two formulas, it can be obtained:

x+2y=280

x+z=150

Equation 2 for yellow flowers

4x+12y+18z

18x+18z+6x+12y

18(x+z)+6(x+2y)

Red, yellow, purple.

A 15 24 25

B 10-12

C 10 18 25

A + C = 3750 25 = 150 formula.

15 A + 10 B + 10 C = 2900, that is, 3 A + 2 B + 2 C = 580 formula.

=4A+2B+3C=580+150=730.

Yellow flower = 24 A + 12 B + 18 C = 6 (4 A + 2 B + 3 C) = 730 6 = 4380.

x-20=y+151

x=y+151+20=y+171 (1)

Substituting (1) to the second equation obtains.

y+171)*(y+15)=(y+171)*y, and y=x=

There are two types of bottles, each with X and Y bottles.

x：y=3：5

Solution x=3000

y=5000

A: These shampoos should be divided into 3,000 large bottles and 5,000 small bottles.

Set: large bottle x bottle, small bottle y bottle.

x/y=3/5

600x+300y=3300000【3300000ml=3300 liters】So x=3y 5

2x+y=11000

So 6y 5+y = 11000

So 11y 5 = 11000

So y=5000

So x=3y5=3000

So 3000 bottles for large bottles and 5000 bottles for small bottles.

Let the large bottle be x and the small bottle be one, then according to the title:

x:y=3:5

It can be solved with x=600 and y=1000