Math problems, prawns in! Middle school math problems. Prawns in

This question can be set to the volume of the cup as a, then it can be obtained: because the orange juice is full at the beginning, so the orange juice is originally a, drink 30% a orange juice, fill up with water, then add 30% a water, drink 25% a, and fill it again, so this time add 25% a water, drink 45% a, and fill it again, then this time add 45% a water, and finally drink it, so a total of 30%a + 25% a + 45% = 100% a water is added, because 100% a water is added in the whole process, and all of them are drunk, so drank a glass of water, and orange juice was also a drink, so drank as much orange juice as water.

I hope it can help you, it's hard to play by hand, don't copy 、、、

Solution: Suppose the volume of this cup is 100ml, then.

In the end, it was not difficult to get Xiaohong to drink all the orange juice, that is, the orange juice consumed 100ml. And Xiaohong drank all the water she had added.

1) Drink 30% of the orange juice first, fill up with water: add 30ml of water.

2) drank another 25% of this cup; After refilling with water: Add 25ml of water.

3) drank another 45% of this cup; Finally, fill up with water and drink: add 45ml.

A total of 100ml of water was added, and 100ml of orange juice was also drunk, so Xiaohong drank the same amount of orange juice as the water she drank.

Solution: Xiaohong drinks 1 cup of orange juice and drinks 30% + 25% + 45% = 100%, that is, 1 cup, so Xiaohong drinks as much orange juice as water.

Lots of water. Tangerine juice: 30% + 25% + 45% = 100% i.e. 1 cup of orange juice.

Whereas. Water: 30% + 25% + 45% + 100% = 200% 2 cups of water.

Solution: Let the straight line ab be y=ax+b

The coordinates of points A and B are (8,0), (0,6) a=-3 4, and b=6, respectively

The straight line ab is y=-3x 4+6

1) Let the straight line oc be y=ax+b

Point C is the point A and B coordinates of the line segment AB, which are (8,0) and (0,6), respectively, and C is (4,3).

o（0,0）

a=3/4，b=0

The straight line oc is y=3x 4

The coordinates of point p are (t,-3t 4+6) pbo, i.e., the triangle s pbo=pd*ob 2=6*t 2=3t, and when point p is in the fourth quadrant, it is.

POA is the triangle that is sought.

s poa=oa*pe 2=8*(-3t 4+6) 2=24-3t, let PE cross oc at point F

The coordinates of OE=T P are (T,-3T 4+6) and the coordinates of F are (T,3T 4)S=S Poe-S Foe

s△poe=pe*oe/2

s△foe=fe*oe/2

s=3t-3t^2/4

3)s=3t-3t^2/4=3(t-t^2/4)=-3[(t/2)^2-2(t/2)]=-3[(t/2)^2-2*(t/2)+1-1]

3[(t 2-1) 2-1]=-3(t 2-1) 2+3 The maximum value is obtained when t 2=1, i.e., s=3 when t = 2

This should be a problem in the third year of junior high school, the process keyboard should not be written, the guiding idea is as follows:

1. There is the Pythagorean theorem to obtain the length of ab, and c is the midpoint to obtain the coordinates of point c from the median line theorem;

2. The intersection method is used to find the M coordinates of the intersection point of PE and OC, and the area formula is used to find the S=S POE-S OEM, that is, the quadratic relationship;

3. Since the value range of t is greater than or equal to 0 and less than or equal to 8, and then determine the maximum value problem in the quadratic function according to the relationship in 2, it is best to solve it in combination with the drawing image, so that the intuitive should not be lost.

(1)y=4/3x

2)p(t,6-3/4t)

Let PE and CE cross 0 points.

s=1 3) when t=36 25, when s=54 25 is maximum.

Solution: 1 From the coordinates of the two points A and B, we can see that the coordinates of the key C of ab are (4,3) Let the analytical formula of the line oc be y=kx

Bringing in the coordinates of c yields: 3=4k solution k=

The analytic formula for the straight line oc is y=

2. Let the line PE and the line OC intersect with the point Q

Let the analytic formula of the straight line ab be y=kx+b

Bringing in the coordinates of the two points of a and b can be solved to obtain the expression of k= b=6 and the straight line ab is y=

OE=XP=T P on a straight line AB.

The coordinates of p are (t, and the required s is the area of pqo.

In the first case, when the abscissa of p is less than the abscissa of c xp=xq=t q, on the straight line oc.

The coordinates of q are (t,pq=

s=(In the second case, when the abscissa of p is greater than the abscissa of c.

Let the PD be at the OC junction point G

The required s is the area of the pgo.

yp=yg=

Substitute it into the analytic expression of the linear OC.

The coordinates obtained by g are (-t+8, gp=t+t-8=2t-8

s=(t-4)*(

3 The first case (could it be that lz has not learned quadratic functions?) This is known from the knowledge of quadratic functions.

When t=-b2a=2 s, the maximum value is 3

The second case.

When t=6, the maximum value of s is 3

To sum up, the maximum value of s is 3 (in fact, the maximum value of s can be guessed in this problem), that is, the maximum value of s is 3 in both cases

I don't know which mock question it is, but the solution of 0228 upstairs is more complete.

1.The volume of a square piece of iron with an edge length of 10 cm is folded into a length of 50 cm. The height behind the cube with a width of 40 cm is the height of the reduction.

20-10*10*10 50 40=cm.

2.(kg.)

3.The diameter of the largest cone is the edge length, and the height is also the edge length.

20*20*cubic centimeters.

2.(πr^2+2πr*h)*

3.The volume of the wooden block is 20 3 = 8000

The diameter of the largest cone is equal to the edge length of the block, i.e. the volume of the cone is *10 2*20=2000

So the volume of the cut part is 8000-2000

Untie. 1.Let the purchase price of Toy A be X yuan, and the purchase price of B toy will be Y Yuan, according to the title.

x+y=40

90/x=150/y

Solving the system of equations yields x=15, i.e., y=40-x=25

The purchase price of a type of toy is 15 yuan, and the purchase price of a type B toy is 25 yuan.

2.Set up M pieces of A toys and n pieces of B toys, so that the total funds of this purchase do not exceed 1,000 yuan, according to the topic.

m+n=48

15m+25n＜1000

Solved n 28

Therefore, when the purchase of B toys is less than 28 pieces, the total purchase funds of the shopping mall do not exceed 1000 yuan (such as the purchase of 27 B toys, the purchase of A toys = 48-27 = 21 pieces, the total purchase of funds = 21 * 15 + 27 * 25 = 990 yuan 1000 yuan, so meet the conditions).

1) Solution: Let the purchase price of toys A and B be x and y respectively, then it will be derived from the title

x+y=40

90/x = 150/y

From the above two formulas, it is obtained: x=15 y=25, that is, type A: 15 yuan, type B: 25 yuan.

2) Solution: Let the number of toys A and B be m and n respectively, then the meaning of the title is obtained:

m+n=48

M can be obtained from the above three formulas m = 23, n = 25 or m = 22, n = 26 or m = 21, n = 27, or m = 20, n = 28, take one of the schemes m = 23, n = 25, that is, the number of purchases of A, B two kinds of toys are 23 and 25 respectively, and the total purchase funds are: 970 yuan.

1) Set the purchase price of each type A and B toys respectively x, yx + y = 40

90/x=150/y

The solution is x=15 and y=25

The purchase price of each type A and B toys is 15 yuan and 25 yuan respectively.

2) A into 23 pieces, B into 25 pieces, a total of 48 pieces.

23x15 + 25x25 = 345 + 625 = 970 yuan.

1) Solution; Let the purchase price of A be x yuan, and the purchase price of B be y yuan x+y = 40; 90 x=150 y gives 5x=3y; x=40-y;200- 5y=3y;8y=200;y=25;x=15 (2) Dissolve into A x pieces, B y pieces. x+y=48,25x+15y=1000.The solution is x=20 and y=28

Set the purchase price A x B y

x+y=40

90÷x=150 ÷y

Solution. x=15

y=25 Number of pieces A A B B

a+b=48

A solution yields a=23

b=25

Think of the retail price in 2003 as 1

The retail price in 2004 was 1+25%=

The retail price in 2005 was 1+10%=

The retail price in 2005 was lower than in 2004 ().

Dizzy! I look left and right, up and down, far and near, but I don't see the question, where is the question?

Tough! The question is in my heart, and the answer is also in my heart.

The retail price in 2004 is higher than in 2003** (1+25%)

The retail price in 2005 was higher than that in 2003** (1+10%)

The percentage of price reduction in 2005 compared to 2004 is 1-(1+10%) (1+25%)=

The guy should have paid it over, so everyone paid 9 yuan, 3 9 = 27, plus the 3 yuan returned, a total of 30 yuan.

Give the boss 25 yuan, 2 yuan for the guy, 1 yuan per person!

Pay 9 yuan per person, a total of 27 yuan.

The boss and the guy split the boss 25 yuan + the guy 2 yuan = 27 yuan.

Then again, that guy is so immoral.

This is a logical calculation problem, if you think about it according to the idea of the question, it is easy to get dizzy, you might as well not think about where the yuan goes, think they pay 10 yuan per person, and then be refunded 5 yuan by the boss, :3*10-5=25They paid a total of 25, and then the guy took another 2 yuan from it, and then they each got 1 yuan, 25 + 3 = 28, which means that the three of them paid a total of 28 yuan, then each of them paid:

28 divided by 3 = instead of 9 yuan per person as stated in the question. It's pushed backwards, the three of them paid a total of 28, plus the guy's 2 yuan, just 30, and that one yuan is actually an approximate number.

Do you mean the total number of people remains the same?

Solution: The number of people in Group A is half of the number in Group B.

Let's make Group A reduce x number of people.

Then 2(28-x) = 20+x

Solution: x=12

The number of people in Group B is half of the number in Group A.

Set up group B to reduce the number of y people.

then 28+y=2(20+y).

Solution: y=4

In summary, when group A has 12 fewer people or group B has 4 fewer people, the number of people in one group is half that of the other group.

1 There are x people in group A.

x+2x=28+20

2 There are Y people in Group A.

There are two solutions to this problem in y+.