F.3 MATHS 問題

2012-10-03 7:21 am

我想問幾條數
想搵人答一答我 THX!

1.The width and the length of a rectangle are in the ratio 2:5. If the width of the rectangle is increased by 25%, what should be the percentage change in the length of the rectangle so that
(a) its perimeter remains unchanged?
(b)its area remains unchanged?

25. A television station broadcasts 16 hours every day. 20% of the time is for advertisements, 40% for news and 40% for music programmes. If the daily broadcast time remains unchanged, but the total time for advertisements and news is increased by 20%, what is the percentage decrease in the time for music programmes?

回答 (1)

micatkie

2012-10-03 9:16 am

✔ 最佳答案

1.
(a)
Let 2k and 5k be the original width and the original length respectively.
Let a be the new length when width is increased by 25%.

2[2k(1 + 25%) + a] = 2(2k + 5k)
5k + 2a = 14k
2a = 9k
a = 4.5k

Percentage change in length
= [(4.5k - 5k)/5k] x 100%
= -10%

(b)
Let 2k and 5k be the original width and the original length respectively.
Let b be the new length when width is increased by 25%.

2k(1 + 25%) x b = 2k x 5k
2.5kb = 10k²
b = 4k

Percentage change in length
= [(4k - 5k)/5k] x 100%
= -20%

=====
25.
Let m hours be the new time for music programmes.

16 x 20% x (1 + 20%) + 16 x 40% x (1 + 20%) + m = 16
3.84 + 7.68 + m = 16
m = 4.48

Original time for music programmes
= 16 x 40% hours
= 6.4 hours

Percentage decrease in the time for music programmes
= [(6.4 - 4.48)/(6.4)] x 100%
= 30%

參考: micatkie

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