Comprehensive application of mathematics, comprehensive application of mathematics

1) From the problem, it can be seen that the master assembles 3 units every day, does a day and rests for 3 days, that is, 3 units can be configured in 4 days, that is, 3+1=4 (days) The apprentice assembles 1 unit every 3 days, and does three days and rests for 1 day. It is also 4 days to configure three sets 3+1=4 (days) and then use the apprentice's plus the master's 24 divided by (3+3)=4 4 times 4=16 (days).

2) For example, if there are 43 machines, divide 43 by 6 = 7 and leave 1 for one more day, so the number of days is 7 times 4 + 1 = 29

The efficiency of the master is: 3 sets for 4 days.

The efficiency of the apprentice is: 1 unit for 4 days.

Time required to assemble 24 machines = 24 (3 4 + 1 4) = 24 days.

Time required to assemble 43 machines = 43 (3 4 + 1 4) = 43 days.

Assuming that it takes at least x days to produce 24 machines, then on the last day, both master and apprentice are working, and on day x-1 the master assembles ((x-1) 4)*3 machines, the apprentice assembles ((x-1) 4)*1 machines, and on day x, the master assembles 3 machines and the apprentice assembles 1 machine.

So: ((x-1) 4)*3+((x-1) 4)*1+3+1=24

x=21

The picture is not clear, and it is better to be troublesome.

1.Use the number method. Suppose the distance from A to B is 120 km.

120 (120 2 30 120 2 60) = 40 (kmh) 2Solution: If he runs 1 lap in x seconds, he will run 2 laps for a total of 800 meters.

4x＋5x=800

9x=800

x=800／9

He ran 400 2 5=40 (seconds) in the second half and 800 9 40=440 9 (seconds) in the first half

4、a²=96×12=12×8×12=12^2×8=12^2×2^2×2=24^2×2

So, a = 24 2cm

5. From the Pythagorean theorem: the square of the hypotenuse = (2 3+1) 2+(2 3-1) 2

26So, hypotenuse = 26

6、x=√5-1

So: x 2+5x-6=( 5-1) 2+5( 5-1)-6=(6-2 5)+5 5-5-6

Suppose 12 years ago, the son was x years old, and the father was 4x years old, there is (x+12)+(4x+12)=69

i.e. 5x=45, x=45, 5=9

So now the son is 9 + 12 = 21 years old, and the father is 4 * 9 + 12 = 48 years old.

(69-12x2) (1x4).

99 ten 12 = 21 (son) years old.

69-21 = 48 years (father).

1.Oral arithmetic. 6 8 72 9 20 300 66 25 39 26 52 60 14 170 90 35 5 4 Mengqing 40 8 24 6 320 70 30 56 7 56 29 7 9 6320 320 52 (22 9) 2

Vertical calculations. 340 520 760 280 460 270 820 570