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 profit, the number of pieces sold by A Electric Appliance was only 5/6 of that in the first quarter, but the total profit was the same as that in 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.
put on file