The answer to 〉〉〉〉〉〉〉〉〉〉〉〉〉〉〉〉〉〉〉ԑ12 There was once a widow who wanted to separate her ex-husband's 3500 yuan inheritance from her children. According to the law at that time, if there was only one son, the mother could get half of the son's share. If there is only one daughter, the mother can get twice the inheritance of her daughter. But she has twin children, a boy and a girl. According to the law at that time, how should she divide the inheritance?
The answer is that the inheritance of mother, son and daughter is X, Y and Z respectively, according to the meaning of the question.
X+Y+Z=3500 ①
X= 1/2Y ②
X=2Z ③
Y = 2x4from ②, z =1/2x5from ③, substitute ④ ⑤ into ①, X= 1000 into ④, Y=2000 into ⑤, and Z=500. Therefore, the inheritance of mother, son and daughter is 1000 respectively.
Christmas Turkey Problem (USA) Westerners regard Christmas as their most important holiday. Before Christmas, John, Peter and Rob went to the market early in the morning to sell their turkeys. These turkeys weigh about the same, so they are only sold. Among them, John has 10, Peter has 16 and Rob has 26. In the morning, three people sold it at the same price. After lunch, because all three people sell it. It had to be sold at a reduced price, but the price of three people was still the same. At dusk, all their turkeys were sold out. When they counted the money, they were surprised to find that everyone got 56 pounds. Think about it, why? What are their prices in the morning and afternoon? How many turkeys did each person sell in the morning and afternoon?
If John, Peter and Rob sell X, Y and Z turkeys in the morning, they will sell 10-X, 16-Y and 26-Z turkeys in the afternoon. If the price is one pound in the morning and one pound in the afternoon, the following equation can be drawn from the meaning of the question:
ax+b( 10-x)=56 ①
ay+b( 16-y)=56 ②
az+b(26-z)=56 ③
This is an indefinite system of equations with five unknowns, but only three equations.
①-③ Get (x-z) (a-b) = 16b，④
②-③ Get (y-z) (a-b) = 10b，⑤
(x-z)/(y-z)=8/5, that is 5x+3z = 8y. ⑥.
According to the conditions of the topic, 0 < x < 10, 0 < y < 16, 0 < z < 26. After substituting into ⑥ test, we can find that only x=9, y=6, z= 1 is the only set of solutions, and then substitute the values of X, Y and Z into ①.
Sun Bin and Pang Juan are both disciples of Guiguzi. One day Guiguzi thought of this question:
He chose two different integers from 2 to 99, told Sun the product and told Pang the sum.
Pang said: I'm not sure what these two numbers are, but I'm sure you don't know what these two numbers are either.
Sun said: I really didn't know at first, but after listening to your words, I can confirm these two figures now.
Pang said, since you put it that way, I know what these two numbers are.
Because Pang Juan determined that two numbers would not both be prime numbers, the sum of the two numbers would not be even. Otherwise, according to Goldbach's decimal conjecture, a small even number would be divided by the sum of two odd prime numbers, and Pang Juan could not be sure that Sun Bin did not know the answer. So the sum of two numbers should be odd. In addition, these two numbers will not be 2 and an odd prime number.
Sun Bin can know two odd and even numbers from Pang Juan's speech. The form of 2^a.b should be the product of two numbers known in Sun Bin, where a >；; 0 and b are odd numbers. For example, b can be decomposed into b=cd, c >；; 1, d > 1, the answer may be (2 a, b), (2 a.c, d) or (2 a.d, c), and the answer is still unknown, so b is a prime number. But from what Pang Juan said above, a> 1.
After Pang Juan spoke from Sun Bin, if the sum of two numbers is unique in the form of 2 A+B, he can also get the answer.
The above reasoning is not comprehensive, but more than one set of answers can be obtained. Examples are as follows:
(4, 13)
Pang Juan knew that x+y= 17, and that x and y can't both be prime numbers.
Sun Bin knew that xy=52. Before listening to Pang Juan, (x, y) might be (2,26), (4, 13). But now we know the parity only (4, 13).
Pang Juanzhi's (x, y) will not be (2, 15)[ because 30 = 2 *15 = 6 * 5 =10 * 3], nor will it be (6,11).
But there are other possibilities, such as
(16, 13) Pang Juanzhi 29, Sun Binzhi 208.
(4,37) Pang Juanzhi 4 1, Sun Binzhi 148.
(16,37) Pang Juanzhi 53, Sun Binzhi 592.
(16,43) Pang Juanzhi 59. Sun Bin knows the interesting topic of the ancient equation of China in 688-Hundred chickens problem. At the end of the 5th century A.D., China mathematician Zhang Qiujian put forward a famous indefinite equation problem-"Hundred chickens problem" in his calculation.
There is a chicken Weng today, worth five; One mother hen is worth three; Chicks, chicks are worth one. You can buy a hundred chickens for every hundred dollars. What are the geometric figures of chicken, Weng and chicken? Supplement-2006-07-0317: 53:10 This question can be described as: a cock is worth five pence, a hen is worth three pence, and three chickens are worth one penny. Now I bought these three kinds of 100 chickens and just spent one hundred pence. There are two shepherds, A and B. A said to B, "Give me one of your sheep. My sheep are twice as many as yours." B replied, "You'd better give me one of your sheep, and our sheep numbers will be the same." How many sheep do two shepherds have each? Tears, the whole city. Answer: If A has X, then B has X-2x+1= 2 * (X-2-1) X+1= 2x-6.