12, Party A and Party B run on the circular road at a constant speed, if they start at the same time. Walk in opposite directions and meet every 2 minutes; If you go in the same direction, meet every 6 minutes. It is known that A runs faster than B. How many laps do A and B run per minute?

Solution: Let A run X laps per minute and B run Y laps per minute. According to the meaning of the question in the equation:

2X+2Y= 1

6X-6Y= 1

X = 1/3 and Y = 1/6 are obtained.

A: A runs 1/3 laps per minute, and B runs 1/6 laps per minute.

13, RMB 100 includes fifty cents, one yuan and two yuan, totaling 100 yuan. The sum of 50 points of 2 yuan is 75 yuan. How much is each kind in RMB?

Solution: Suppose there are five-corner A cards, one-dollar B cards and two-dollar 100-a-b cards.

According to the meaning of the question

0.5a+b+ 2×( 100-a-b)= 100( 1)

0.5a+2×( 100-a-b)=75(2)

(2) Replace (1)

B= 100-75=25 sheets.

Substitute (2)

0.5a+ 150-2a=75

75= 1.5a

a=50

So there are 50 50 yuan tickets, 25 Zhang Yiyuan tickets and 25 binary tickets.

14, both parties brought some money. If Party A gets half of Party B's money, then Party A has a total of 50. If Party B gets two-thirds of all the money, then Party B will have a total of 50. Q: How much did Party A and Party B bring?

Solution: suppose a brings money a and b brings money B.

a+ 1/2b=50( 1)

b+2/3a=50(2)

simplify

2a+b= 100(3)

3b+2a= 150(4)

(4)-(3)

2b=50

B=25 yuan.

A=50-25/2=37.5 yuan

A brought 37.5 yuan, and B brought 25 yuan.

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