1. A store sells discount cards. When 20 yuan buys this card, she can shop in this store at a 20% discount. Gao Xiao saved 5 yuan money by buying a card. What is the total price (original price) of shopping in Gao Xiao?

Let the original price be X X-0.8X-20=5 and the solution be X= 125.

2. There are 150 students planting trees in a certain grade. On average, boys dig two tree pits every day, while girls don't plant four trees every day. This makes it possible to plant trees in every tree pit. How many boys and girls are there in this grade?

Suppose there are x girls and 2x boys: x+2x = 150. Get 50 girls and 0 boys 100.

3. Weight of a barrel of oil 12kg. After pouring out half of the oil, the remaining oil and barrel weigh * * * 7kg. How many kilograms of oil is in the original barrel and how many kilograms does the barrel weigh?

Let the oil be x kg and the barrel be y kg, then x+y= 12 x/2+y=7 and x= 10 y=2.

4. If the sum of two angles is 130 degrees and the difference between two feet is 10 degrees, find the degrees of these two angles.

∠a+∠b = 130∠a-∠b = 10 ∴∠a=70∠b = 60

5. The original price of a commodity is 33 yuan. The store adjusts the price of goods and sells them at 10% of the original price. At this time, the profit rate of goods is 10%. What is the purchase price of this commodity?

Let the purchase price be x, 0.9×33-x= 10%x and x=27.

6. There are 64 workers in workshop A and B and 38 workers in workshop B, so the same number of workers need to be transferred from the two workshops, so the number of remaining workers in workshop A is twice that of workshop B, with three more workers. How many workers do you need to transfer from workshop A and workshop B?

Suppose that X workers need to be transferred from workshop A and workshop B, 64-x=2(38-x)+3. The solution is x= 15.

7. The purchase price of an air conditioner is 1800 yuan. According to the forecast, if you sell 2000 yuan/set, you can sell 520 sets. If the price increases by 1 yuan, the sales volume will decrease by 10 sets. If you want to make a profit of 504 thousand, how much is the price of each air conditioner reasonable?

If the price of each air conditioner is X yuan, increase (X-2000)/ 100 times 100 yuan on the basis of 2000 yuan; So we sold less 10*(X-2000)/ 100 units; The net profit of each air conditioner is X- 1800 yuan.

{520-[10 * (x-2000)/100} * (x-1800) = 504000 according to the known conditions.

Simplified to x square -9000X+ 18000000=0.

The solution is X=6000 or X=3000.

So when each air conditioner sells for 6000 yuan or 3000 yuan, it can earn 504000 yuan.

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