(1) How much is it per catty after the price reduction in early April?
(2) Find the monthly average growth rate of pork price in May and June.
Solution: (1) Let the pork price in early April be one yuan.
60/x+2=60/(2/3x)
60/x+2=90/x
30/x=2
X= 15 yuan
(2) let the average growth rate be b.
15×2/3×( 1+b)？ = 14.4
( 1+b)？ = 1.44
1+b= 1.2 or 1+b=- 1.2.
B=0.2 or -2.2 (truncated)
The average growth rate is 20%
2 1. hongxing primary school used 480 kwh of electricity in September, one-ninth more than that in September. /kloc-How many kWh was used in October?
Set the electricity consumption of 10 to kWh.
(a-480)/480= 1/9
9a-480*9=480
9a= 10*480
A= 1600/3 kwh
22. For a photo with a length of 29cm and a width of 22cm, it is required that the four sides of the photo frame have the same width, and the area occupied by the photo frame is one quarter of that of the photo frame. What is the width of the photo frame?
Solution: Let the width be one centimeter.
According to the meaning of the question
(29+2a)×a×2+22×a×2 = 1/4×29×22
4a？ +58a+44a=3 19/2
8a？ +204a-3 19=0
a=(-5 1 √3239)/4
A=(-5 1-√3239)/4 (omitted)
therefore
a =(-5 1+√3239)/4≈ 1.48cm
23. A farmer grows peanuts, and the original peanuts yield 200 kg per mu, and the oil yield is 50% (that is, 50 kg of peanut oil can be processed per 100 kg of peanuts). Now, after planting new peanut varieties, the harvested peanuts per mu can be processed into peanut oil 132 kg, in which the growth rate of peanut oil output is half of that per mu. Seeking the growth rate of yield per mu of new peanut varieties.
Solution: We assume that the yield growth rate per mu of new peanut varieties is a.
Then the oil yield is 1/2a.
200×( 1+a)×50%×( 1+ 1/2a)= 132
(a+ 1)(a+2)= 132/50
Answer? +3a+2-2.64=0
Answer? +3a-0.64=0
simplify
25a？ +75a- 16=0
a=(-75 85)/50
A=-3.2 (truncated) or a=0.2=20%
Therefore, the yield per mu of new peanut varieties increased by 20%.
24. If the purchase price of goods in 40 yuan is increased by 25%, 500 goods can be sold. If the future price increases by 1 yuan, the sales will decrease by 10. If the profit is 8000 yuan, and both merchants and customers are profitable, what should the selling price be? How much should I buy this?
Solution: Price =40×( 1+25%)=50 yuan.
The cost is 40× 500 = 20,000 yuan.
If the price goes up by one yuan, the 10a units will be sold less.
According to the meaning of the question
(50+a)×(500- 10a)-40×(500- 10a)= 8000
25000-500a+500a- 10a？ -20000+400a=8000
10a？ -400a+3000=0
Answer? -40a+300=0
(a- 10)(a-30)=0
A= 10 or a=30.
When the price is raised 10 yuan or 30 yuan, the profit will be 8,000 yuan, but in order to win-win, the price should be raised 10 yuan.
At this time, the stock is 500- 10× 10=400.
1, bring 200 kilometers of water into the city. This task was handed over to two construction teams, A and B, with a construction period of 50 days. After 30 days of cooperation between the two teams, team B had other tasks to go 10 days, so team A speeded up and repaired 0.6 kilometers more every day. In order to ensure the construction period, team B 10 will come back in 0 days. Q: How many kilometers did Team A and Team B originally plan to build?
Solution: Let's assume that the original speeds of Party A and Party B are A km and B km per day respectively.
According to the meaning of the question
(a+b)×50=200( 1)
10×(a+0.6)+40a+30b+ 10×(b+0.4)= 200(2)
simplify
a+b=4(3)
a+0.6+4a+3b+b+0.4=20
5a+4b= 19(4)
(4)-(3)×4
A =19-4× 4 = 3km.
B = 4-3 = 1 km
A repairs 3 kilometers every day, and B repairs 1 kilometer every day.
A It was originally planned to build 3× 50 = 150km.
B 1× 50 = 50km as originally planned.
2. Xiaohua bought four mechanical pencil and two pens, and paid 14 yuan; Xiaolan bought the same 1 mechanical pencil and two pens, and paid 1 1 yuan. Find the unit price of mechanical pencil and pen.
Solution: Suppose mechanical pencil has a pen with X yuan and a pen with Y yuan.
4X+2Y= 14
X+2Y= 1 1
The solution is X= 1.
Y=5
In mechanical pencil, the unit price is 1 yuan.
Pen unit price 5 yuan
3. According to statistics, in 2009, the profit rate of commercial housing sold by builders in a certain area was 25%.
(1) What is the cost of a commercial house with a total selling price of 600,000 yuan in this region in 2009?
(2) In the first quarter of 20 1 0, the price per square meter of commercial housing in this area increased by 2 yuan, and the cost per square meter only increased by1yuan, so the area of commercial housing that can be purchased for 600,000 yuan decreased by 20 square meters compared with 2009, and the profit rate of builders reached one third, thus seeking the profit per square meter of commercial housing sold by builders in this area in 20 10.
Solution: (1) Cost = 600/(1+25%) = 480,000 yuan.
(2) In 2000, we set the price at 2,065,438+600,000 yuan to buy B square meters.
Cost of commercial housing in 20 10 year = 60/(1+1/3) = 450,000.
60/b-2a=60/(b+20)( 1)
45/b-a=48/(b+20)(2)
(2)×2-( 1)
30/b=36/(b+20)
5b+ 100=6b
B= 100 m2
The house price per square meter in 20 10 year =600000/ 100=6000 yuan.
Profit = 6000-6000/(1+1/3) =1500 yuan.
4. A store sold several pieces of A-type electrical appliances at the original price (cost+profit) in the first quarter, and each piece earned an average profit of 25%. In the second quarter, due to a slight increase in profits, the number of sales of Class A electrical appliances was only 5/6 of that of the first quarter, but the total profit was the same as that of the first quarter.
(1) What is the average profit per piece of Class A electrical appliances sold by this counter in the second quarter?
(2) In the third quarter, the counter sold 90% of the price in the first quarter. Therefore, the number of pieces sold increased by 65,438+0.5 times compared with the first quarter. What percentage is the profit of Class A household appliances sold in the third quarter higher than that of Class A household appliances sold in the first quarter?
Solution: (1) Let the cost be A, the number of pieces sold be B, and the profit rate in the second quarter be C.
Then profit =a×25%= 1/4a.
In the second quarter, 5/6b electrical appliances were sold.
Total profit in the first quarter = 1/4ab
Profit in the second quarter =ac×5/6b=5/6abc
According to the meaning of the question
1/4ab=5/6abc
c= 1/4×6/5
c=3/ 10=30%
(2) Pricing in the first quarter =a( 1+25%)=5/4a.
Pricing in the third quarter =5/4a×90%=9/8a
Sold (1.5+ 1)b=2.5b pieces in the third quarter.
Total profit in the third quarter =9/8a×2.5b-2.5ab=5/ 16ab.
Total profit growth in the third quarter (5/16ab-1/4ab)/(kloc-0//4ab) = (116)/(1/4) = 0.25.
5. Put some chickens in some cages. If there are four chickens in each cage, there is no cage for one chicken; If you put five chickens in each cage, there is only one cage without chickens. So, how many chickens and cages are there?
Suppose there are x chickens and y cages.
4y+ 1=x
5(y- 1)=x
Get x=25, y=6.
6. Make tin cans with tin foil. Each tinplate can be made into 25 boxes or 40 boxes. A box body and two box bottoms can be made into a set of cans. There are 36 iron sheets. How many pieces can I use to make the box and the bottom just match?
Analysis: Because there are always 36 iron boxes, x+y=36. Formula; The number of sheets made in the box+the number of sheets made at the bottom of the box = the total number of sheets made in cans * * * 36. The equation (1) is obtained. Because now a box body and two box bottoms are made into a set of cans, so; Number of boxes *2= number of box bottoms. This will make them equal. Equation (2)2* 16x=40y is obtained.
x+y=36 ( 1)
2* 16x=40y (2)
36-y=x (3) from ( 1)
Substituting (3) into (2) to obtain;
32(36-y)=40y
y= 16
If y= 16 is substituted (1), then x=20.
So; x=20
y= 16
Answer: Use 20 sheets as the box, and 16 as the bottom.
for reference only