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Mathematical problems of alloys
Zinc, copper and nickel are mixed into different alloys, and the weight ratio of zinc, copper and nickel in the first alloy is 2: 3:1; The second alloy has a ratio of 2: 4: 3; The ratio of the third alloy is 1: 2: 1. Now, these three alloys are mixed into another alloy, so it contains 10g zinc, 18g copper and 10g nickel. How many grams are used for each of the three alloys?

The first alloy: zinc: copper: nickel = 2: 3: 1 = 4: 6: 2.

The second alloy: zinc: copper: nickel = 2: 4: 3 = 4: 8: 6.

The first alloy: Zn: Cu: Ni =1:2:1= 2: 4: 2.

Another alloy: zinc: copper: nickel = 10: 18: 10.

Each serving: (10+18+10)/(4+6+2+4+8+6+2+4+2) =1(g)

The first alloy is 1x(4+6+2)= 12 (g).

The second alloy is 1x(4+6+8)= 18 (g).

The third alloy is 1x(2+4+2)=8 (g).

Someone rode a bicycle from place A to place B, and at first, he drove at the speed of 18km per hour. When the remaining distance was 32 kilometers less than the distance he had traveled, he began to walk the remaining distance at a speed of 25 kilometers per hour. If the average speed of the whole journey is 20km per hour, how to find the distance between A and B?

Solution: Let the remaining distance be X kilometers and the driving distance be x+32 kilometers.

x/25+(x+32)/ 18 =(x+x+32)/20

36x+50(x+32)=45(2x+32)

36x+50x+ 1600 = 90x+ 1440

4x= 160

x=40

Distance between Party A and Party B: 40+40+32= 1 12 (km).

15.5-0.4(x+3)= 3/4x-2/5(x-5)

15.5-0.4x- 1.2 = 3/4x-2/5x+2

3/4x= 12.3

x= 16.4