maths一問!!!!

Question

如果氣油的價格上漲20%, 用戶必須多省百分幾的耗油量才能令支出維持不變????

Answer 1

設用戶原來的氣的價格 = x
用戶原來的耗油量 = y
用戶原來的支出 = xy
用戶現在的支出 = ( 1 + 20%)xy = 1.2xy
設用戶必須多省z%的耗油量才能令支出維持不變
1.2x ( 1 - z%)y = xy
( 1 - z%)xy = 5xy / 6
1 - z% = 5 / 6
1 - z% = 0.8333333.. = 83. 33% (corr. to 2 dp)
z = 16.67% (corr. to 2dp)
用戶必須多省16.67%的耗油量才能令支出維持不變

Answer 2

Let $P be the price per cubic meter and Q be the cubic meter consumed
x% be the % decreased in volume consumed

Therefore, total expenditure = P*Q = PQ
Now, P increased by 20% and total expenditure needed to be remain the same

P(1+20%)* Q(1-x%) = PQ
1.2(1+x%) = 1
(1+x%) = 0.833333
x% = -0.167
x=-16.7%

Therefore, they must decrease quantity consumed by 16.7%

Answer 3

支出=價格*耗油量
If new 價格=1.2 old 價格
new 支出= old 支出
new 耗油量
= new 支出/new 價格
= old 支出/1.2 old 價格
= ( 5/6) old 支出/old 價格
= (5/6) old 耗油量
= (1-1/6) old 耗油量
必須多省 16.67%(1/6) 耗油量才能令支出維持不變

Answer 4

let the original price be x,the consumption of oil be y
the new price =x(1+20%)
let z be the answer of the question
x(1+20%)*y(1-z%)=xy
1.2(1-z%)=1
z=16.666..
所以要節省16.66666...%

Answer 5

設所求百分率為x,

(1+20%)(1-x) = 1
所以, 1.2 - 1.2x = 1
1.2x = 0.2
x = 1/6= (50/3)%