Two Olympiad questions, added to 120 points!

1. Set AB to be at a distance of x km.

Derived from the drive time being equal.

Find x.

2. Let the meeting time of B and C be x minutes, then the distance between B and C can be obtained: the distance between AB is 40x+50x

Similarly, the meeting time of A and C is increased by ten minutes, and the distance between AB is 30 (X+10) + 50 (X+10), from which the equation is 40X+50X=30(X+10)+50(X+10), and X=8 is obtained, then the distance of AB is 720 meters.

Question 1: Let the two stations of A and B be n kilometers apart, and the equation according to the question is: n (54+48) 54 3 48 3) = 216

Solution: n=1224

Question 2: (2 solutions).

Solution 1: Let the distance be s when C meets B x then it takes.

s=40x+50x

s=(30+50)(x+10)

Solve the above system of equations.

Get s=7200

Solution 2: 40 50) [30 50) 10 (40-30)] = 7200 (m).

Thank you, the ordinary equation is the first question.

The second problem can be solved with solution 2.

If the height of the water is h, the water volume of the water tank is 40 30 h = 1200h (cubic centimeters).

The volume of water in tank B is 30 20 h = 600h (cubic centimeters), and the volume of raw water is: 30 20 24 = 14400 (cubic centimeters), then: 14400 = 1200h + 600h

Solution: h=8cm

It can be seen from the title.

After pouring water, the ratio of the volume of water tank A and B is.

Therefore, the volume of water in tank A is (30*20*24) 3*2=9600, and the depth is: 9600 (40*30)=8cm

You see that the total volume of water in B is 30*20*24=14400, and then the total volume of the two of them is 14400, and let their height: h

Then h(40*30+30*20)=14400h=8, the answer is revealed..

Good luck!

1.Let p(x)=x*g(x)+a

then p(19)=19*g(19)+a=1994(a).

p(94）=94*g(94)+a=1994 (b)

b)-(a)=>19*g(19)=94*g(94)

Because it is an integer polynomial, g(19) and g(94) are both integers, and 19 and 94 are coprime, so g(19) must be a multiple of 94, and g(94) must be a multiple of 19, so we can set :

g(19)=94*m

g(94)=19*m

Substituting formula (a).

19*94*m+a=1994

a=1994-1786*m

a0｜＜1000 =>|1994-1786*m|<1000

994<1786*m<2994 (m is an integer).

m can only be equal to 1

Therefore a = 1994-1786 = 208

2.Add the following guides:

Because both the angle p and the angle q are right angles, for aepq, the angle e + angle a < 180 degrees, and the angle e and the angle a must have an angle less than 180 2=90, assuming a.

The perpendicular line of Pd through point C intersects AE at point K, the perpendicular line of ed through point D intersects Ak at point N, and the perpendicular line of ed through point A intersects Ak at point M.

ck is perpendicular to dp, so ck is parallel to ab, and in the same way as is parallel to bq

AMCB is a parallelogram.

BC=AM triangle CDN is a right triangle, > CDAS parallel DN, angle NMS "angle A<90 degrees, it can be seen that in the trapezoid: DN=》BC+CD=>BC+CD and the triangle ase is a right triangle, AE is hypotenuse.

as=> bc+cd, so the original question is proven.

1.Let the constant term of p(x) be a0, then p(x) x q(x)+a0 where q(x) is the integer polynomial, so p(19) 19n+a0p(94)=94m+a0, where m and n are integers

From p(19)=p(94), we get 19n=94m, so n=94k, m=19k (k is an integer).

So 19 94K+A0=1994, from which we get A0=1994-1786K

Because a0 is 1000, k=1 and a0=208

Set the purchase price to be $ x and the selling price to be $ y.

Then the upper formula and the lower formula =

That is, y = 3300 yuan, substituting the above formula to know the destruction of Yu filial piety x = 3900 yuan.

The purchase price is 3900 yuan.

The red ones are x, and the yellow ones are y.

Then x 3 + above Eq. 2 gives the destruction of x+2y 3=260

Equation 3 gives x+

Subtracting the following formula gives 5y 6=100

i.e. y=120

Substituting a formula for a sub-fiber manuscript gives x=180

That is, 180 red and 120 white.

x=3300

Yuan) Red 2 + Yellow 3 = 130 3 Red + 2 Yellow Buried Fiber Calendar = 780 Red 3 + Yellow Bend Search 2 = 120 2 Red + 3 Yellow = 7205 Red Vertical Mu + 5 Yellow = 1500 Red + Yellow = 300 2 Red + 2 Yellow = 600 Red = 180 Yellow = 120

1。Set the purchase price to x, 9% off to earn 210 yuan, if 80% off 120 yuan, then the price of 19% off minus 8% off (x + 210) - (x-120) = 330, into the old slide key, 330 * 8 + 120 = 2760 yuan.

2.。There is a red x and a yellow y.

x 2+y let volt 3=130, x 3+y 2=120 get x=180, y=120

Column binary system of equations.

1.Solution: Set the purchase price to be $ x, and the current price is $ y.

The solution is x=2760, y=3300

A: The purchase price is 2760 yuan.

2.Solution: Set x red balls and y white balls.

50%x+1/3y=130

1/3x+50%y=120

The solution is x=180, and the talk is y=120

Answer: There are 180 red balls and 120 yellow balls.

Absolutely, trust me!

Hopefully!

1 solution: The price of the bent tomb is X yuan Wang God before being buried.

x=3300

So the purchase price is.

1. Set the selling price to be Huaichun x yuan, and the purchase price to be y yuan, Hu Ming imitates it; x=3300 y=2970

2 Let the red pants have x, the yellow has y, 1 3x+ x=180 y=120

Analysis: Situation 1: If each question is 8 points, and no points will be deducted for incorrect answers, his total score should be 72 + 4 * the number of questions answered incorrectly; Scenario 2:

If each question is 12 points, and no points will be deducted for incorrect answers, his total score should be the situation plus the number of questions answered correctly * 4, that is, 72 + 4 * the number of questions answered incorrectly + the number of questions answered correctly * 4;Let the original question be Situation 3, and the score of Situation 2 is 4 more than the score of Situation 3 * the number of questions answered incorrectly + the number of questions answered correctly * 4, i.e. 15*4

Therefore, the original question (situation 3) is equivalent to 12 points for each question, and no points will be deducted for incorrect answers, and his total score is 15*4+72, so the number of questions he answered correctly is (15*4+72) 12=11

The tail length is equal to half of the head length plus the head length plus the tail length, so the tail length is (3 + 3) (2-1) = 6, and the body length is 9, so the total length is 3 + 6 + 9 = 18 meters.

The total area is 4 * 3 * 2 + 3 * 3 * square meters, and the bending needs to be painted, < 5, so at least 5 barrels are needed, about 286 * 5 = 1430 yuan.