F.1 Maths (只答1條也no problem)20點

👨🏻‍🏫 學術台數學

[匿名]

2012-08-01 9:55 pm

1. Roy has 200 mL of orange juice, 200 mL of apple juice and 100 mL of grape juice in his kitchen. H wants to make a glass of 300 mL mixed juice for his mum. She
prefers that there are least 40% orange juice and at most 50% apple juice in the mixed juice. Suggest the volumes of each kind of juice he should use.

2.Peggy goes to the swimming pool every two fays. Daisy goes to the same
swimming pool every three days. If they met at the swimming pool on Monday,
when will they meet again？

3.Paul is using a string of length 60 cm to form a rectangle. What are the length
and the width of the rectangle so that its area is greater than 200 cm2？

更新1:

THANKS!

更新2:

Peter Chow, Sorry,can you write the most correct steps in the number 3? it's because I need to write the steps on my homework. Thx for your answer.

回答 (2)

PeterChow

2012-08-01 10:17 pm

✔ 最佳答案

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.'

參考: me

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用戶46949

2012-08-02 6:28 pm

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)

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