Two math problems to solve immediately in 20 minutes

Person X in Person A 4x<50<5x x = 11 or 12 Person B Person Y 3y<50<4y 50 412<=y<=16 From the meaning of the title, A can only be 11 B 16

There are x dormitories.

The number of people is 4x+19

4x+19 =6(x-1) +a (a=1,2,3,4,5)Simplify: 2x=25-a A can only be an odd number (1,3,5) When a=1 2x=24 ->x=12 the number of people is 67a=3 x=11 the number of people is 63

a=5 x=10 The number of people is 59

1: Set group A x people, group B y people, because group A if each person is straight four, then the tree is not divided so x 12, and each person 5 trees is insufficient, so x 11, and if each person is straight three, then the tree is not finished, so y 16, and because y=x+5 so x=11, y=16

1. Let A and B be x and y respectively.

Yes. 4x<50

5x>50

3y<50

4y>50

x+5=y, 10y

Solution: 19 2 so x=10,11,12

y=59,63,67

1.If A has x people, then B is x+5 people.

From the inscription: 4x<50, 5x>50, (5+x)3<50, (5+x)4>50

Solving the above relationship between x can clearly show that x=11 is 11 people in group A and 16 people in group B.

1.Solution: Let the copper weigh 7x grams and the zinc weigh 5x in the original alloy, and the equation can be listed

7x+5x+7=67, the solution is x=5, so the copper in the new alloy is: 7x=35 (grams), zinc is: 67-35=32 (grams), and the ratio is:

2.Solution: Let A's existing deposit be 14x yuan, then B's existing deposit is 25x yuan, and the equation can be as follows: 14x+210=(1+2 5)25x, and the solution is x=10, 14x=140, so A's existing deposit is 140 yuan.

Question 1: Let the original copper-zinc alloy copper be 7x, then zinc is 5x, then get: 7x+(5x+7)=67, x=5, so copper is 35 grams, zinc is 32 grams, and the ratio of copper to zinc in the new alloy is 35:32

Question 2: Let B's deposit be x, then we get: (7 5x—210): x=14:25 solution x=250, so now A's deposit is (7 5*250)—210=140 yuan.

The calculation is hard, and the hope is for!

The content of zinc in the new metal is: (67-7)*5 (5+7)+7=60*5 12+7=32 grams.

The amount of copper in the new metal is: 67-32 = 35 grams.

The ratio of copper to zinc in the new alloy is: 35:32

Let copper be 5x and zinc be 6x, then 5x+6y+7=67, and solve x=5 then 25 grams of copper and 35 grams of zinc.

Question 1: Solution: Set the length to xcm

The width is ycm by the title Liang Travel Know.

x+4)(y-1)=xy①

x-2)(y+1)=xy②

Simplification of Jingchang stool, de.

4y-x=4

2y+x=2

Solve the binary equation and get.

x=8 y=3

The length is 8 cm and the width is 3 cm

S length = 8 3 = 24 (cm).

Question 2 (Come back and think about it, write this quick start first).

(1) Solution: Set the cost of this dress to be X yuan.

Cost Cost 40 selling price.

x＋x×40％＝560

x＋x＝400

A: The cost of this dress is 400 yuan.

In question 2, it should have been 2|sinx|However, since the meaning of the question is from 0 to 2, sinx is non-negative, and the absolute value sign is omitted.

It's an integral question, and it's not very difficult to go back and check the points table

1. Square defg dg=de=hm=6 cm dg ef am=ah+hm=4+6=10 cm dg bc

ADG ABC AH AM=dg bc bc=am·dg ah=10 6 4=15 cm.

2. Make ag bc in g and de de f de bc s abc s ade

s△abc:s△ade=(ag·bc):(af·de)de:bc=af:ag=2:5

s△abc:s△ade=25:4

s△ade=20×4÷25=16/5

Question 1: According to the meaning of the topic:

1. The square defg is the inscribed square of the triangle ABC One side of the square falls on one side of the triangle.

2. Am is perpendicular to BC to M, and Dg to H DG does not fall on one side of the triangle.

3. According to the above points, it can be divided into: (1) EF falls on a certain side of the triangle. (2) :d e or gf (these two sides have the same meaning) falls on one side of the triangle, i.e., ef does not fall on one side of the triangle.

1) When:ef falls on one side of the triangle:

defg is a square dg parallel ef ah:dg = am:bc, and because ah is 4 CM LONG, THE SIDE LENGTH OF THE SQUARE IS 6 CM, DG 6 cm, AM 4 cm + 6 cm 10 cm.

Substituting ah=4 cm, dg 6 cm, and am 10 cm into ah:dg=am:bc, we get 4:

6 10: BC BC 15 cm.

2) When DE or GF (these two sides have the same meaning) falls on one side of the triangle, that is, EF does not fall on one side of the triangle, the conditions are insufficient and there is no solution.

Question 2: DE is parallel to BC, DE and AB intersect D, and AC intersects E

S triangle abc:s triangle ade bc*bc:de*de, substitute de=2, bc=5, s triangle abc=20 into the above equation to obtain:

20:S triangle ade 5*5:2*2 20:S triangle ade 25:4 S triangle ade 20*4 25 s triangle ade 16 5

1.Let the length of BM be A, the length of CM be B, the length of DH be C, and the length of GH be D, the area of the triangle ABC = the area of the triangle ADG + the area of the trapezoidal DHMB + the area of the trapezoidal GHM, so there is: BC*AM*1 2 =DG*AH*1 2 + DH+BM)*HM*1 2 that is, (A+B)*(4+6)*1 2=(A+B)*5=6*4*1 2 +(C+A)*6*1 2 + D+B)*6*1 2=12+(c+a+d+b)*6*1 2=12+(6+a+b)*6*1 2=30+(a+b)*3, the solution is a+b=15

So the BC is 15 cm long.

2.Since the two triangles ABC and ADE are similar, the corresponding area ratio ABC:ADE=(DE:BC) 2=25:4, because the area of the triangle ABC is 20, the area of the triangle ADE is 16 5