數學percentage 問題!4條 F3

1. On travelling over the same distance, if the speed is increased by 25%, what is the percentage change in the time taken?

Distance = speed x time
Distance is constant. That does not change
Distance = speed (1.25) x time (D)
D = 1 – percentage change in time (in decimal form)
If distance remains constant, 1.25 x D = 1
D = 1/1.25 = 0.8
The time must decrease by 20%

2. If the length of a rectangle is increased by 10% and the width is decreased by 40%, find the percentage change in the area of the rectangle
A1 = length x width
A2 = 1.1 length x 0.6 with = 0.66 length x width = 0.66 A1
The percentage change (100 – 66) = 34% decrease in the area.

3. An alloy, which contains 70% iron and 30% aluminium,weighs 20kg. If the manufacturer adds 5 kg copper into the alloy, what percentages are iron,aluminium and copper in the new alloy respectively?
Weight of iron = 20 kg x 30% = 20 x 0.3 = 6 kg
Weight of aluminium = 20 kg x 70% = 20 x 0.7 = 14 kg
Weight of copper = 5 kg
Total wt. = 20 kg + 5 kg = 25 kg
% of iron = 6/25 x100% = 24%
% of aluminium = 14/25 x100% = 56%
% of copper = 5/25 x100% = 20%

4. Mr Chiu's total monthly expenditure on housing, food and transportation is $
10000, they are in the ratio 5:2:3. If the housing expense is reduced by 20%,whiile the food and transportation expenses are increased by 10% and 8% respectively,find
a) his new total expenditure on housing,food and transportation,
b) the percentage change in his total expenditure on the above three items

Old cost housing = $10000 x 5/(5+2+3) = = $10000 x 5/10 = $5000
Old cost food = $10000 x 2/(5+2+3) = = $10000 x 2/10 = $2000
Old cost Transport = $10000 x 3/(5+2+3) = = $10000 x 3/10 = $3000

New cost housing = $5000 x 0.8 = $4000
New cost food = $2000 x 1.1 = = $2200
New cost Transport = $3000 x 1.08 = = $3240
 
(a)Total new expenditure on housing,food and transportation
= $4000 + $2200 + $3240 = $9440

(b) % change = ($10000 -$9440)/10000 x 100%
= 560/10000 x 100%
= 5.6% decrease