a(350- 10a)-2 1(350- 10a)= 400
350a- 10a^2-7350+2 10a=400
a^2-56a+775=0
(a-25)(a-3 1)=0
A=25, price increase = (25-21)/21*100% =19%.
A=3 1, price increase = (31-21)/21*100% = 47.6% > 20%, (irrelevant)
2. A clothing factory produces a batch of clothes for the school art troupe, with a total cost of 3,000 yuan. The price is 30 yuan per set. Students from 24 poor families are provided free of charge. After accounting, the cost of these 24 sets of clothing is exactly the profit of the original production of this set of clothing. How many sets of clothes have been made?
(3000+30*24)/30= 124 pieces
3. A fruit wholesale market sells a high-grade fruit. Profit per kilogram 10 yuan, you can sell 500 kilograms every day. According to market research, if the price per kilogram increases by 1 yuan, the daily sales will be reduced by 20 kilograms. Now the market should guarantee a profit of 6000 yuan per day. At the same time, it is necessary to give profits to customers, so how much is the price increase per kilogram?
If we want to benefit our customers, we should increase the price by X yuan per kilogram.
( 10+x)(500-20x)=6000
5000-200x+500x-20x^2=6000
x^2- 15x+50=0
(x-5)(x- 10)=0
X 1= 10, x2 = 5< 10, (customers get benefits), then the price per kilogram will be increased by 5 yuan.
4. The school is going to build a rectangular carport with an area of 50 square meters on the side of the field behind the library, and at the same time use the back wall of the library and the existing iron railing with a total length of 25 meters. Please design and how to build it correctly.
Let a rectangular carport be x in length and 1/2(25-x) in width.
1/2(25-x)*x=5
x^2-25x+ 100=0
X=5, (inappropriate, railing length is not enough)
X=20 (appropriate, the railing length is just enough)