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Sixth grade mathematics thinking questions
1. Two people are working on the same part. One hour is more than three hours, and seven hours is less than nine hours. How many do Party A and Party B make every hour?

Answer: let a be X.

B is X-3.

X*7=(X-3)*9-3

X= 15

2. In quadrilateral ABCD, angle B is 70, angle C is 90, BC=CD, AB=AD, and how many degrees is angle A?

Answer: The drawing shows that angle B is equal to angle D, so angle A is 360-90-2*70= 130.

It takes 6 hours for Party A to do a job alone, and 4 hours for Party B to do a job alone. After A finishes 1/3, how many hours will they need to cooperate?

Solution: Let the total workload be 1, and A has already completed 1/3, so there are still 2/3 unfinished.

The work efficiency of Party A is 1/6, and that of Party B is 1/4. Two people work together.

The efficiency is1/6+1/4 = 5/12, so the remaining 2/3 needs to be completed.

(2/3)/(5/12) = (2/3) * (12/5) = 8/5 =1.6 (hour).

For this kind of problem, we only need to understand the relationship between the following three quantities: total workload Q and work efficiency. ※

Rate η, working time t: q = η t, (equivalent to S=Vt in the distance problem)

η=Q/t,t=Q/η。 In calculation, the total workload is often set to 1.

4. The number of boys in Class 6 (1) last semester was 5/3 of that of girls, and two girls were transferred this semester. Now the number of boys in Class 6 (1) is 3/2 of that of girls. How many boys were there in Class Six (1) last semester?

Solution: Suppose there were X boys and 3x/5 girls last semester, then there is an equation:

x \u( 3x/5+2)= 3 \u 2

That is 2x=3(3x/5+2).

10x=3(3x+ 10)

X=30, which means there are 30 boys.

The fruit shop brought in a batch of fruits, accounting for 5/8 of the total, and then 700 Jin. Now the fruit in the fruit shop is exactly 2/3 of the original. How many kilograms did the fruit shop have?

Solution: Let the original fruit be x kg, and there is an equation according to the meaning of the question:

( 1-5/8)x+700=2x/3

3x/8+700=2x/3

9x+ 16800= 16x

7x= 16800

∴ x = 16800/7 = 2400kg

That is, the original fruit is 2400 Jin.

6. Xiaoming's age this year is 2/7 of his father's age and 5/ 16 of his mother's age. His father has always been three years older than his mother. How old is Xiaoming this year?

Solution: Suppose Xiaoming is X years old, then Xiaoming's father is 7x/2 years old and Xiaoming's mother is 16x/5 years old.

Then the equation 7x/2- 16x/5=3.

That is, 35x-32x=30

3x=30

X = 10 years old.

That is, Xiaoming 10 years old.

7. Each internal angle of a regular polygon is 20 greater than its adjacent complementary angle. What is the sum of the internal angles of this polygon?

Answer: The complementary angle of the inner angle is (180-20)/4=40, so the inner angle 140 is a positive nonagon.

The sum of internal angles is 140*9= 1260.

8. If the minimum internal angle of a polygon is 120 and slightly larger than its internal angle is 125, then each internal angle is 5 times larger than the previous internal angle, and the ratio of the maximum internal angle to the minimum internal angle is 4: 3. How to find the number of sides and the degree of the maximum internal angle of this polygon?

Answer: The maximum internal angle is 120/3*4= 160.

The number of edges is (160-120)/5+1= 9.

9. Party A needs 65,438+00 hours, Party B needs 65,438+02 hours and Party C needs 65,438+05 hours to move the goods in the warehouse. There are the same warehouses A and B. Party A is in warehouse A, and Party B is moving goods at the same time. At first, Party C helped Party B to move the goods, but in the middle, it turned to Party A.. All the goods in the last two warehouses were handled at the same time, and Party C helped Party A and Party B respectively.

Solution: Because warehouse A and warehouse B are the same, and because warehouse A needs 10 hour to move.

B needs 12 hour, and C needs 15 hour.

It is known that the total workload of warehouse A is the least common multiple of 10, 12 and 15.

[ 10, 12, 15]=60

So A is 6 per hour, B is 5 per hour and C is 4 per hour.

So the total workload of warehouses A and B is 60×2= 120.

To do it at the same time, all three people should do it.

120 ÷ (6+5+4) = 8 hours

So c is like a gang.

(60-6× 8) ÷ 4 = 3 hours

Such as c and B.

(60-5×8)4 = 5 hours

10. The cost of commodity A is 80% of the price, the price of commodity B is 275 yuan, and the cost is 220 yuan. Now the store sells one commodity A and two commodities B together at 90% of the sum of their prices. So this set can be profitable. What is the cost of commodity A in 80 yuan?

Solution: suppose the price of commodity A is X.

(x+2*275)*0.9-0.8x-220*2=80

(x+550)*0.9-0.8x-440=80

0.9x+495-0.8x-440=80

0. 1x+45=80

0. 1x=80-45

X=250

250*0.8=200

A: The cost of commodity A is 200.