Unary Equation Problem Solving Comes Soon There is a high reward

Let's be more careful.

When the water is smooth. Speed = speed of the boat + speed of the water.

When the water is against the water. Speed = speed of the boat + speed of the water.

The speed of the boat is x, and the speed of the water is yColumn Equations:

When the water is downstream: x+y=20 1

Against the current: x-y=16 2

Add 1 to 2 to get :

2x=36x=18

Substituting x=18 into 1 yields:

18+y=20

y=2 so the answer is: The speed of water is 2 kilometers per hour.

There are many ways. There are simpler ones. You can think for yourself.

You want a dollar at a time. Let's think about the above first. before it is listed.

Let the velocity of the water be x, because the velocity of the boat is the same when it is going forward and against the water, then you can set the equation: 20-x=x+18

The solution is x=2

You should have read it. The children are so happy now, but no one answered when we wanted to ask. Parents are busy, or they don't know.

Will you shake me? Let the ship speed x, the water speed y, x+y=20, x-y=16, and the solution is x=18, y=2

2 kilometers, this is a quadratic equation? I don't know, I taught it in the second grade of elementary school, and I listed what to do.

Solution: Let the water flow speed be x kilometers per hour, which can be obtained from the title.

20－x=16+x

2x=20-16

2x=4x=2

A: The water flow speed is 2 kilometers per hour.

20-x is the speed of the ship in still water, that is, the speed of the ship in the water velocity = the speed of the ship in still water.

16+x is also the speed of the ship in still water, that is, the speed of the ship against the water + the speed of the water = the speed of the ship in still water.

So 20-x and 16+x are equal

Got it?

Set the water velocity to x kilometers per hour.

20－x=16+x

x=2 The speed of the water is 2 kilometers per hour.

Set the water velocity to x kilometers per hour.

Downstream speed Boat speed Water speed Boat speed Downstream speed Water speed.

Speed against the water Boat speed Water speed Boat speed Water speed Water speed Water speed.

20－x=16+x

x=2 The speed of the water is 2 kilometers per hour.

Because sailing speed along the water = hydrostatic speed + current velocity, sailing speed against the water = hydrostatic velocity - current velocity.

Suppose that the water velocity is x km/h.

Equation 20-x-x=16 is solved to x=2 km hours.

1.If the ** can be reduced to x yuan, then (1500-1000-x) 1000 5% will be sorted out, and 1500-1000-x 50 x can be reduced by up to 450 yuan, and the profit margin can be guaranteed to be not less than 5%.

1) The purchase price of the piece with a profit of 25% is 60 (1+25%)=48, and the purchase price of the piece with a loss of 25% is 60 (1-25%)=80

2) The profit of the 25% profit is 60-48=12, and the profit of the 25% loss is 60-80=

3) Selling these two clothes, in general, is 12 + (-20) = -8, that is, a loss of 8 yuan.

(1) Solution: Suppose that the per capita net income of rural residents in China in 2005 is X yuan.

x=3255

Answer: In 2005, the per capita net income of rural residents in China was 3,255 yuan.

2) 3255* RMB).

Answer: After deducting the first factor, compared with 2005 in 2006, the actual increase in the per capita net income of rural residents in China was 241 yuan.

Li Jun bought a 5-year construction bond of 1,000 yuan, and he was able to get a total of yuan of principal and interest after maturity. What is the annual interest rate of this kind of bond?

1.There are a total of 834 people in the two villages, and the number of people in village A is 111 fewer than half of the number in village B.

2.A car and an electric car set off from two places 298 kilometers apart at the same time, and the speed of the car was 15 kilometers more than six times the speed of the electric car, and they met half an hour later. Find the speed of two cars.

3.Someone shared 142 yuan to buy two kinds of fruits for a total of 20 kilograms, it is known that fruit A is 8 yuan per kilogram, and fruit B is 6 yuan per kilogram, and asks how many kilograms of these two fruits are there?

4.Enclose a rectangle with a rope 80m long so that its width is 1 3 long, what should be the length and width of each?

5.A boat sails between the two piers, taking 10 hours against the water and 6 hours downstream. The vessel is known to travel 12 kilometers per hour in still water, and the speed of the current and the distance between the two piers are determined.

6.A project, A alone 20 days to complete, B alone 10 days to complete, now B alone for a few days, the rest of the part by A alone, has been completed in 12 days, ask B how many days?

1. Solution: Set up X people in Village B.

1／2x－111＋x＝834

3／2x＝945

x 630630 2 111 204 (person).

A: There are 204 people in Village A and 630 people in Village B.

2. Solution: Set the speed of the electric vehicle x kilometers.

x 8383 6 15 513 kmh

A: The speed of the electric car is 83 km/h, and the speed of the car is 513 km/h.

3. Solution: Set X kg of A fruit.

8x＋6（20－x）＝142

8x＋120－6x＝142

2x＝22x＝11

20 11 9 (kg).

A: 11 kg of fruit A and 9 kg of fruit B.

4. Solution: set the length x meters.

2（x＋1／3x）＝80

8／3x＝80

x 3030 3 10 (m).

A: It is 30 meters long and 10 meters wide.

5. Solution: When the water velocity is x kilometers.

10（12－x）＝6（12＋x）

120－10x＝72＋6x

16x＝－48

x 310 (12 3) 90 (km).

Answer: When the water speed is 3 km, the distance is 90 km.

6. Solution: Set B to do x days.

1／10x＋1／20（12－x）＝1

2x＋12－x＝20

x 8 A: B did it for 8 days.

You see for yourself a lot and the answers.

Let bag B weigh x kg of rice and bag A of rice (3x) kg.

According to the title, there is 3x=x+5The solution is x = kilograms.

Therefore, it turned out that the bag of rice was 3*kg. A bag of rice kilograms.

Then put 5 kg of rice in bag B, which weighs the same as the two bags. then A is 5 kg heavier than B.

B originally had 5 (kg) of rice.

A originally had 25* kilograms of rice.

Set the original bag of rice x kg.

3x=x+5

x=3*

Let bag B weigh x kg 3x=x+5 x=5/2 A = 5/2 multiplied by 3.

A75, B.

Let B be x, then A is 3x, and from the question, 3x x+5 gives x

1. There are x acres of river slopes. Column equation: 1000*80%+300+20%x=(1000+x+300)*60%.

Solution: 800+300+20%x=600+60%x+18020%x-60%x=600+180-300-800-40%x=-320

x=320*100/40

x=800A: There are 800 acres of river slope land.

Analysis: The equivalence relationship is: the area of all greenery is equal, and the amount of greenery in part is equal to the total amount of greenery.

2. The customer purchased a product worth X yuan in the course of consumption. Column equation: 50 + (x-50) * 9 10 = 212 (x-50 is the excess multiplied by 9 10 is the money after the discount.) ）

Solution equation: 50+(x-50)*9 10=212 Solution: 50+9 10x-50*9 10=21250+9 10x-45=212

9/10x=212+45-50

9/10x=207

x=207*10/9

x=230A: The customer purchased a product worth 230 yuan during consumption.

The key to the application of unary equations is to find the equivalence relationship.

1.Set the area of river slope land as acres.

1000 80%+300+20% =60% (1000+300+) x=800

The river slope is 800 acres.

2., purchased a value of goods, get.

The equivalent relationship or something, you need to dissect it step by step, it is not something that can be done in a short time, because you are not very skilled, maybe others do it much faster than you, but you still have to calm down and think slowly, refer to formulas, read more math books, understand the example problems in the book, learn more, do more, come on!!

The key here is to find the equivalence relationship, and it is best to draw a graph to help understand it at first. Generally related to the process of movement (travel, encounter, chase, etc.), you just look at their movement trajectory, if it is in a circle (running on the playground, cycling, etc.) you draw a circle, mark the relative position of the characters on the diagram, as much as possible to reflect the known information on the diagram (help to find the equivalent relationship), and then find the equivalent relation; If their trajectories are straight lines, such as in highways, rivers, etc., you draw straight lines to represent them, and also mark their relative positions, and then find the equivalent relation. (Note that the quantities you set ( ) and the physical quantities that can be represented by the quantities you set are also considered known conditions, and if you can, they are also marked on the auxiliary diagrams), all in order to find the equivalence relation.

What to do with the problem of tailwind and headwind? To answer this kind of question, speed is the key, just like the problem in water, downwind speed is the speed in the windless + wind speed The upwind speed is the speed in the windless - the wind speed, so for example, if the wind speed is known to be a, if you set the speed in the windless to x, then the downwind speed is +a, and the upwind speed is -a, both of which are known, and can be substituted as known in the column equation.

Finally, practice a lot and you will improve.

Have fun and hope it helps.