The ratio problem of (1) three numbers: common assignment methods

If A: B = A: B, B: C: D,

Then a a: b: c = ac∶ bc∶ bd

(2) the growth rate problem: commonly used valuation methods.

B=a( 1+x)n (let the basic variable be a, the average growth rate be b, and the final value be b).

2. Travel problem: distance = speed * time

(1) Meet: the speed of A * time+the speed of B * time = the sum of distances.

(2) Catch-up: catch-up time = catch-up distance * speed difference

(3) Delay: actual time-delay time = planned time

(4) Early arrival: actual time+early arrival time = planned time.

(5) the problem of relative speed

(1) oncoming, speed; In the same direction, the speed is subtracted.

(2) Navigation problem: speed along the water = ship speed+water speed; Current speed = ship speed-water speed

3. Engineering problems: work efficiency = workload/working time

(1) Common equivalence relation: sum of workload of each part+unfinished workload = total workload = 1.

(2) Water supply and drainage: original water quantity+inflow = displacement+residual water quantity.

4. Profit problem

(1) profit = cost of sales

(2) Profit rate = profit/cost × 100%

5. Liquid problem: concentration = solute/solution × 100%

Solution matching problem: mix two solutions with different concentrations into another solution by cross method.

Step 6 set questions

(1)A or B=A+B-A and b.

(2)A or B or C=A+B+C-A and B-A and C-B and C+A and B and C.

7. The most valuable application problems

(1) According to the meaning of the question, it is transformed into a quadratic function of one variable to find the maximum value.

(2) According to the meaning of the question, turn it into a mean inequality to get the maximum value.

(3) According to the meaning of the question, it is transformed into solving inequality problems.