New observation on the first volume of seventh grade mathematics 70-7 1 answer

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 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.