F2 inequalities 數

1. On a highway, car A and car B travel in an opposite direction from each other from the same starting point. The speeds of cars A and B are 75km/h and 85km/h respectively. How long (in min) will it take for cars A and B to be at least 40km apart?

A. Let the time taken for cars A and B to be at least 40km apart be y hour.
85y+75y ≦ 40
160y ≦ 40
y ≦ 40/160
y ≦ 1/4

Therefore, the time taken for cars A and B to be at least 40km apart is 60/4 = 15 mins

2. A store bought 250 eggs for $200 and found that 25 of them were cracked. The rest of the eggs will be sold at a percentage profit of not greater than 35%. Find the maximum selling price of each egg.

A. Let the selling price of each egg be $y
(250-25)y-200 /200 *100% ≦ 35%
225y-200 /200 ≦ 35%
225y-200 ≦ 0.35*200
225y-200 ≦ 70
225y ≦ 70+200
225y ≦ 270
y ≦ 270/225
y ≦ 1.2
Therefore, the maximum selling price of each egg is $1.2

3. The ingredients of the nuts of Brand X, Brand Y and Brand Z in percentage are as follows:

Brand X Y Z
Walnut 30% 25% 55%
Almond 30% 50% 30%
Hazelnut 40% 25% 15%

How many kg of nuts from Brand Z should be added to 0.5kg of nuts from Brand X and 1kg of nuts from Brand Y, such that there are not less than 20% of hazelnuts in the mixture?

A. Let z kg of nuts from Brand Z should be added to 0.5kg of nuts from Brand X and 1kg of nuts from Brand Y, such that there are not less than 20% of hazelnuts in the mixture.

[(15%)z+0.5(40%)+1(25%)]/(z+0.5+1) ≧ 20%
0.15z+0.2+2.5 ≧ 0.2(1.5+z)
0.15z+2.7 ≧ 0.3+0.2z
0.05z ≧ 2.7-0.3
0.05z ≧ 2.4
z ≧ 48

Therefore, 48 kg of nuts from Brand Z should be added to 0.5kg of nuts from Brand X and 1kg of nuts from Brand Y, such that there are not less than 20% of hazelnuts in the mixture.

以上問題請詳解.