3 long F3 Maths questions

用戶40721

2013-11-25 4:26 am

1.The student union of a school organizes a fund-raising ball every year. Last year, 180 students attended the ball. The ticket price of the ball was $50 and the total cost was $3500. Suppose the number of students who attend the ball is increased by 20% and the total cost is increased by 25% this year.
If the students' union wants an increase of 30% in the amount of funds raised as compared to last year, what should be the percentage in the ticket price? (cor. to 2 sign. fig.)

2.Paul drives from X to Y at an average speed of 60 km/h for t hours. He then has to co
mplete another journey which is 20% longer than the distance between XY, but in a tie 10% less than t hours. If Paul drives at an average speed to complete the second journey, what is the percentage increase in his speed?

3. A certain liquid is placed in a rectangle container. After heating, both the length and the width of the container increased by 2%. At the same time, the volume of the liquid inside increased by 10%. Find the percentage change in the depth of the liquid. (cor. to 1 decimal place)

answer of Q.1 :6.7%
Q.2 : 33/1/3%
Q.3 : 5.7%
Plz give me the full steps. Thank you very much!!!!!!!!!

回答 (1)

用戶4366

2013-11-25 8:23 am

✔ 最佳答案

1. Last year :
180 students
Total ticket price = 180 X $50 = $9000
Total cost = $3500
Fund raised = 9000 - 3500 = $5500

This year :
Number of student = 180 X (1+0.2) = 216
Total cost = $3500 X (1.25) = $4375
Fund raised = $5500 X (1.3) = 7150

Ticket price = ($7150 + $4375)/216 = $53.36

($53.36-$50)/$50 = 0.0671 = 6.7%

2. Distance XY = (60)(t) km
Distance (1.2)(XY) = (1.2)(60)(t) = 72t km
Time = (1-0.1)t = 0.9t
speed = Distance / Time
= 72t/0.9t = 80 km/h

(80 - 60) / 60 = 0.3333 = 33.33%

3. Volume = Width X Length X Height
V = W X L X H ............................ (1)
V' = W' X L' X H'
1.1V = 1.02W X 1.02L X H' ....... (2)

(2) / (1) gives

1.1 = 1.02 X 1.02 X (H'/H)

H'/H = 1.05728

Depth is 5.7% increased

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