F.1 Maths (只答1條也no problem)20點

1.
Volume of orange juice=300x40%=120mL(at least)
Volume of apple juice=300x50%=150mL(at most)
Hence, volume of grape juice=300-150-120=30mL
Since all the volumes I suggested do not exceed the volume provided.
Therefore, he should use 120mL orange juice, 150mL apple juice and 30mL grape juice.
2.
The L.C.M. of 2 and 3 is 6.
Therefore, they will meet after six days.
i.e. They will meet on Sunday.
3.
To form a shape with a biggest area, it is better to form a square.
Area of the square=(60/4)^2=225cm^2
However, the question asked for a rectangle.
Therefore, we can translate 1cm to the length from the width.
Hence, the length is 16cm and the width is 14cm.
Area of the rectangle=16x14=224cm^2
Since this rectangle fits all conditions, the length and the width can be 16cm and 14cm respectively.
Other reasonable answers:
13x17
12x18
11x19
Actually, if the length and the width can be decimal numbers, there are infinite numbers of answers.

2012-08-18 14:17:12 補充：
3.
Set up a set of equations with a cm being the length and b cm being the width.
2(a+b)=60---1
ab>200---2
Then solve the equation.
NOTE: Only change subject in equation 1 and substitute into equation 2.
i.e. you cannot say 'from 2, a>200/b and then sub. this value into equation 1.'

3. the length + the width = 60/2 =30
Let x be the length of the rectangle
and (30-x) be the width of the rectangle

x* (30-x) >200
30x -x^2 > 200
x^2 -30x +200 <0
(x-20)(x-10)<0
10 < x < 20

so, the length of the rectangle is between 10 and 20 (e.g. 11, 12, 13.....19)
the width of the rectangle is (30-x) (e.g. 19, 18,17,.......11)