Use equation or arithmetic to solve the following practical problems, and write the equivalent relation 1. The store shipped 4 tons of apples, 3 / 4 less than 2 times of oranges. How many tons of oranges? 2. An engineering team built a highway. It was 38 meters in the first day, and 40 meters in the second day. The second day more than the first day, it was 1 / 28 of the total length of the road. How many meters is the total length of the road?

Use equation or arithmetic to solve the following practical problems, and write the equivalent relation 1. The store shipped 4 tons of apples, 3 / 4 less than 2 times of oranges. How many tons of oranges? 2. An engineering team built a highway. It was 38 meters in the first day, and 40 meters in the second day. The second day more than the first day, it was 1 / 28 of the total length of the road. How many meters is the total length of the road?

Orange * 2-3 / 4 = apple
We are supposed to deliver x tons of oranges
2X-3/4=4
2X=4+3/4
2X=19/4
X=19/4/2
X = 2.375 A: 2.375 tons of oranges
Day 2 - day 1 = 1 / 28 of the total length 2 = 1 / 28x
Suppose the total length is x M. x = 56
40-38 = 1 / 28x answer: the total length is 56 meters

List the equivalent relations and solve the application equations
Please help to list the equivalent relations of the following practical problems:
1. Some students go boating. If there are four people in each boat, there will be thirteen more. If there are six people in each boat, there will be three seats on the boat. Then, how many boats are there? How many students are there
2. The sum of divisor and divisor is 193, the known quotient is 8, and the remainder is 13. What are the divisor and divisor respectively? If possible, give the solution to the equation by the way

Question 1
Equivalent relation: total number of people on board of 4 people per ship + 13 people = total number of people on board of 6 people per ship - 3 people (all equal to the actual total number)
With X ships, the equation is 4x + 13 = 6x-3
x=8
∴4x+13=45
There are 8 boats and 45 students
Question 2
Equivalence relation: divisor × quotient + remainder = divisor
Let the divisor be x and the divisor be 193-x
The equation is: 8x + 13 = 193-x
x=20
∴193-x=173
The divisor is 20 and the divisor is 173

Write the relation of equal quantity according to the following conditions
1. The number of boys is three times less than that of girls
2. Most of the red flowers are three times as big as the yellow ones
3. The weight of eggs and duck eggs is 90 kg
4. The first five hours travel 18 kilometers more than the last three hours

1. Boys = 3 times girls - 2
y=3x-2
2. Safflower = 3 times yellow flower
y=3x
3. Egg + duck egg = 90
y=-x+90
4. The first five hours are y kilometers, and the last three hours are x kilometers
y=x+18

Write the quantity relation according to the condition
(1) Three trucks and five vans carry 18.5 tons of coal
(2) 16 bags of rice is 2000 kg lighter than 50 bags of flour

1. Number of copies × number of copies = total number
Total number of copies
Total number of copies = number of copies
2.1 times × times = several times
How many times △ 1 times = Times
Several times △ times = 1 times
3 speed × time = distance
Distance △ speed = time
Distance △ time = speed
4 unit price × quantity = total price
Total price / unit price = quantity
Total price △ quantity = unit price
5. Working efficiency × working time = total amount of work
Total workload △ work efficiency = working hours
Total amount of work △ working time = working efficiency
6 addend + addend = sum
Sum - one addend = another addend
7 subtracted - subtracted = difference
Subtracted difference = subtracted
Difference + subtraction = subtracted
8 factor × factor = product
Product △ one factor = another factor
9 divisor / divisor = quotient
Divisor / quotient = divisor
Quotient x divisor = divisor
Primary school mathematics figure calculation formula
1 square
C perimeter s area a side length
Perimeter = side length × 4
C=4a
Area = side length × side length
S=a×a
2 cube
5: Volume a: edge length
Surface area = edge length × edge length × 6
S table = a × a × 6
Volume = edge length × edge length × edge length
V=a×a×a
3 rectangle
C perimeter s area a side length
Perimeter = (length + width) × 2
C=2(a+b)
Area = length × width
S=ab
4 cuboid
5: Volume s: Area A: length B: width H: height
(1) Surface area (L × W + L × H + W × h) × 2
S=2(ab+ah+bh)
(2) Volume = length × width × height
V=abh
5 triangles
S area a bottom h height
Area = bottom × height △ 2
s=ah÷2
Triangle height = area × 2 △ bottom
Triangle bottom = area × 2 △ height
6 parallelogram
S area a bottom h height
Area = bottom × height
s=ah
7 trapezoid
S area a upper bottom B lower bottom h height
Area = (upper bottom + lower bottom) × height △ 2
s=(a+b)× h÷2
8 round
S area C perimeter Π d = diameter r = radius
(1) Perimeter = diameter ×Π = 2 ×Π× radius
C=∏d=2∏r
(2) Area = radius × radius ×Π
9 cylinder
v: Volume H: height s; bottom area R: bottom radius C: bottom perimeter
(1) Side area = perimeter of bottom surface × height
(2) Surface area = side area + bottom area × 2
(3) Volume = bottom area × height
(4) Volume = side area △ 2 × radius
10 cone
v: Volume H: height s; bottom area R: bottom radius
Volume = bottom area × height △ 3
Total number △ total number of copies = average number
The formula of sum difference problem
(sum + difference) △ 2 = large number
(sum difference) △ 2 = decimal
The problem of sum times
Sum (multiple-1) = decimal
Decimals × multiples = large numbers
(or sum - decimal = large)
Differential multiple problem
Difference (multiple-1) = decimal
Decimals × multiples = large numbers
(or decimal + difference = large)
The problem of tree planting
1. The tree planting problem on non closed lines can be divided into the following three cases
(1) if trees are to be planted at both ends of the non closed line, then:
Number of plants = number of segments + 1 = total length △ plant spacing-1
Total length = plant spacing × (number of plants - 1)
Plant spacing = total length (number of plants - 1)
(2) if trees are to be planted at one end of the non closed line and not at the other end, then:
Number of plants = number of segments = total length △ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length △ number of plants
(3) if trees are not planted at both ends of the non closed line, then:
Number of plants = number of segments-1 = total length △ spacing-1
Total length = plant spacing × (number of plants + 1)
Plant spacing = total length (number of plants + 1)
2. The quantitative relationship of tree planting on closed lines is as follows
Number of plants = number of segments = total length △ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length △ number of plants
Profit and loss
(profit + loss) △ the difference between the two distributions = the number of shares participating in the distribution
(big profit - small profit) △ the difference between the two distributions = the number of shares participating in the distribution
(big loss - small loss) △ the difference between the two distributions = the number of shares participating in the distribution
Encounter problem
Encounter distance = speed and X encounter time
Encounter time = encounter distance △ speed and
Speed sum = encounter distance △ encounter time
Follow up questions
Pursuit distance = speed difference × pursuit time
Pursuit time = pursuit distance △ speed difference
Speed difference = pursuit distance △ pursuit time
Flow problem
Downstream velocity = hydrostatic velocity + water velocity
Countercurrent velocity = still water velocity - water velocity
Hydrostatic velocity = (downstream velocity + countercurrent velocity) △ 2
Water flow velocity = (downstream velocity countercurrent velocity) △ 2
Concentration problem
Weight of solute + weight of solvent = weight of solution
Weight of solute / weight of solution × 100% = concentration
Weight of solution × concentration = weight of solute
Weight of solute △ concentration = weight of solution
Profit and discount
Profit = selling price cost
Profit margin = profit / cost × 100% = (selling price / cost-1) × 100%
Up and down amount = principal × up and down percentage
Discount = actual selling price △ original selling price × 100% (discount < 1)
Interest = principal × interest rate × time
After tax interest = principal × interest rate × time × (1-20%)