let the total power consumption be x degrees: [(x-14) * .57+14 * .43]/x = .5
.57x-79.8+6.2 = .5x
.7x = 19.6
x = 28. Due to the obvious increase in the purchase of home appliances this summer, the manager of the home appliance department transferred 22 people from the sales staff to deliver the goods. Results The ratio of delivery staff to sales staff was 2: 5. How many delivery staff and sales staff were there in the home appliance department of this shopping mall?
if there are x delivery personnel, there are 8X sales personnel.
(x+22)/(8x-22) = 2/5
5 * (x+22) = 2 * (8x-22)
5x+11 = 16x-44
11x = 154
x = 154.
Suppose: increase x%
9% * (1+x%) = 1
Solution: x = 1/9
Therefore, the sales volume is increased by 11.11% compared with the original price
4. The sum of the original unit prices of two commodities, A and B, is 1 yuan. Due to market changes, A commodity What are the original unit prices of two commodities, A and B?/
Suppose the original unit price of A commodity is X yuan, then B is 1-X
(1-1%) X+(1+5%) (1-X) = 1 (1+2%)
The result is X=2 yuan A
. Find the original number of people in each workshop.
suppose there are x people in workshop B. according to the equality of the total number of people, the equation is listed:
x+4/5x-3 = x-1+3/4 (x-1)
x = 25
so the number of people in workshop A is 25 * 4/5-3 = 17. Both of them are moving at a high speed, so that they can start at 8: a.m. at the same time. By 1: a.m., they are still 36 kilometers apart, and by 12: noon, they are 36 kilometers apart. How to find the distance between A and B? (Equation)
Let the distance between A and B be X
x-(x/4)=x-72
x=288
A: The distance between A and B is 288
7. The length of both cars is 18 meters. If the two trains are driving opposite each other, a: A: B: If driving in the same direction, it takes 6 seconds from the front of a car to the rear of b car, and the speed of the car remains unchanged. Find the speed of a car and b car.
the sum of the two cars' speeds is: [18 * 2]/12 = 3m/s
Let A's speed be X, then B's speed is 3-x
18 * 2 = 6 [x-(3-x)]
X = 18
That is. Light two candles at the same time, and blow them out at the same time when the call comes in. The thick one is twice as long as the thin one, and the power outage time is calculated.
Let the power outage time be X
Let the total length be unit 1, so the thick one burns 1/3 at a time, and the thin one is 3/8
1-x/3 = 2 [1-3x/8]
X. 4
that is, there is a power failure 2. Four hours.
9. A factory produced 2,3 machines this year, which was 25% higher in the first half of the year and 15% lower in the second half. How many machines were produced in the second half of this year?
solution: if x production units are set in the second half of the year, [23-X] units will be produced in the first half of the year.
according to the meaning of the question: 1-15%X+1+25%23-X=23
The solution: 931
A: 931 units will be produced in the second half of the year.
1. A rides a bicycle from place A to place B, and B rides a bicycle from place B to place A, both of them move forward at a high speed, so as to know that they set off at 8 am at the same time, and by 1 am, they are still 36 kilometers apart, and by 12 noon, they are 36 kilometers apart. How to find the distance between A and B? ]
Let the distance between A and B be X
x-(x/4)=x-72
x=288
A: The distance between A and B is 288m
11. The fast horse walks 24 miles every day, and the slow horse walks 15 miles every day. The slow horse walks for 12 days. How many days can the fast horse catch up with the slow horse?
the slow horse walks 15 miles a day, and the fast horse walks 24 miles a day. The slow horse walks for 12 days first, which means that the distance between the slow horse and the fast horse is 15×12=18 miles, and then the fast horse starts, and the fast horse walks 24 miles a day. But when the fast horse chases the slow horse, the slow horse is also walking, so subtract the speed of the fast horse from 24-15=9. The fast horse catches up with the fast horse for 9 miles a day, so 18÷9=2 days is the number of days when the slow horse catches up with the fast horse
12. It is known that five A-type machines have four products left after filling eight boxes a day, and seven B-type machines have one product left after filling 11 boxes a day. Each A-type machine produces one more product than the B-type machine, so how many products are there in each box?
there are x products in each box
5 A-type machines: 8x+4
7 B-type machines: 11x+1
Because (8x+4)/5=(11x+1)/7+1
, therefore: x=12
if the total length is "1", the speed of father is 1/3, and that of son is 1/2
if the catching-up time is X
, father will leave 5 minutes earlier: 1/3 * 5 = 1/6
x [1/2-1/3] First, A worked alone for 5 hours, and then worked with B for 4 hours to complete the task. It is known that A processes 2 more parts per hour than B. How many parts do A and B process each hour?
solution: suppose that b processes (x-2) pieces per hour, then a processes x pieces per hour.
according to the total workload such as work efficiency and multiplication time:
[(x-2)+x] * 4+5x = 2
[2x-2] * 4+5x = 2
8x-8+5x = 2
13x = 2+.
15. The total length of a bridge is 1 meters, and a train passes through it. It is measured that it takes 1 minute for the train to get on the bridge and 4 seconds for the whole train to stay on the bridge completely.
1 minute =6 seconds
Let the train length be x meters. Then according to the meaning of the question, it can be obtained that
the speed of the train is (1+x)/6
, so [(1+x)/6]*4=1-2x
gives x = 125
(1+x)/6 = (. The length is 125m
16. Each worker in a workshop can produce 12 bolts or 18 nuts, and each bolt should be matched with two nuts. At present, there are 28 workers. How to allocate the number of workers to make the daily output just match?
solution: suppose x people are assigned to produce bolts, then (28-x) people will produce nuts
Because each bolt needs two nuts, twice the number of bolts is equal to the number of nuts
2×12x=18(28-x)
The solution is x=12, so 28-x = 28-12. 16 people produce nuts
17. Put sugar in several small squares, 1 in the first square, 2 in the second square, 4 in the third square, and 8 in the fourth square ... And so on, there are 448 * * in three consecutive squares starting from several squares?
it is known that sugar is equivalent to a geometric progression An with a public ratio of 2, And an = 2 (n-1)
requires that there are 448 * * grains in three consecutive cells starting from a few cells. Let the number of sugar in this cell be an, and the sum formula is
[an (1-2 3)]/(1. First, A worked alone for 5 hours, and then worked with B for 4 hours to complete the task. It is known that A processes 2 more parts per hour than B. How many parts do A and B process each hour?
solution: suppose that b processes (x-2) pieces per hour, then a processes x pieces per hour.
according to the total workload such as work efficiency and multiplication time:
[(x-2)+x] * 4+5x = 2
[2x-2] * 4+5x = 2
8x-8+5x = 2
13x = 2+.
19. There are 3 tourists, 1 of whom know neither Chinese nor English. Three people know English three times as much as Chinese. How many people know English but don't know Chinese?
assuming that there are x people who know Chinese, there are 3X+3 people in English
those who know English and those who know Chinese must be greater than or equal to 3-1
3X+3+X > = 3-1 (greater than or equal to)
Those who know English must not exceed 3-1, that is, less than or equal to
3x+3 <; = 3-1
17/4 < = X < =17/3
X=5 people (x must be an integer)
3X+3=18 people
those who know both English and Chinese are 18+5-2=3 people
2. The store sells two sets of clothes, each of which costs 135 yuan, and one of them makes a profit of 25% according to the cost. One set made a profit of 25%, and the other set lost 25%. Are the two sets of total profit or loss
The cost of setting the first set is X
X*[1+25%]=135
X=18
Profit: 135-18=27 yuan
The cost of setting the second set is Y < Deficit: 45-27=18 yuan
21. A cylindrical bucket for drinking water has an inner diameter of 25 cm and an inner wall height of 35 cm. There is a glass with an inner diameter of 6 cm and an inner wall height of 1 cm. How many glasses do you need to put a bucket of drinking water in this glass?
A cylindrical bucket for drinking water has an inner diameter of 25 cm and an inner wall height of 35 cm. There is a glass with an inner diameter of 6 cm and an inner wall height of 1 cm. How many glasses do you need to put a bucket of drinking water in this glass?
suppose: x glasses are needed
3 * 3.14 * 1 * x = 5 * 5 * 3.14 * 35
x = 5 * 5 * 35/3 * 3 * 1
x = 9.7
answer: 1 glasses are needed. It takes six days for the apprentice to do it alone. Now the apprentice does it for one day first, and then two people cooperate. After the completion, the reward is 45 yuan. If the reward is calculated according to the amount of work completed by each person, how should it be distributed?
Let the total workload be X, the master's efficiency be x/4, the apprentice's efficiency be x/6, and the total efficiency be 5x/12. If the apprentice does x/6 in one day, the time for them to complete it together is 5x/6 divided by 5x/12 to get 2 days, which means that it takes a total of 3 days. Every day, it is the efficiency competition between master and apprentice in 15 yuan. The apprentice's money is 12+15=27 yuan
23. In the second quarter, a canteen saved 37kg of coal, of which May saved 2% more than April and June saved 25% more than May. How many kilograms of coal did the canteen save in June?
solution: suppose you save x kilograms in April.
x+(1+2%)x+(1+2%)x+25%*(1+2%)x=37
x+1.2x+1.2x+.25* 1.2x = 37
3.7x = 37
x = 1
June = April *(1+2%)(1+25%)
Then it is equal to:
1 * (1+2%) *.
a: the food.