F.3 Percentage , fast , thx !!

ariel

2013-02-07 6:59 am

1. Sammy mixed alcohol and water in the ratio of 4 : 1 . After a while, 15% of the alcohol in the mixture evaporated . If 30% of the original volume water is added into the mixture .
a) find the ratio of the volumes of alcohol to water in the new moisture.
( hint : Let 4x ans x be the volume of alcohol to water in the new mixture )

b) find the percentage change in the total volume of the mixture

2.S3A is arranging a barbecue where the total expenditure will be shared equally by all participants . If there are 15 participants, each of them has to pay $ 60. If the number of participants increases by x % and 4% of the total expenditure is save , the amount to be paid by each participants will decreases 20 % , find the value of x

Please list out all steps , thank you !!!

回答 (1)

用戶2053

2013-02-07 7:29 am

✔ 最佳答案

1a)Let 4x and x be the volume of alcohol to water in the new mixture. After a while, 15% of the alcohol in the mixture evaporated , so
the volume of alcohol in the new moisture = 4x (1 - 15%) = 3.4x.If 30% of the original volume water is added into the mixture ,
the volume of water in the new moisture = x + (4x + x)30% = 2.5x.The required ratio = 3.4x : 2.5x = 34 : 25.
b)% change =

(New volume - Old volume) / Old volume * 100%

=

(3.4x + 2.5x) - (4x + x)
─────────────── * 100%
4x + x
= (5.9 - 5)x / (5x) * 100%
= +18% 2)New number of participants * new paid = new total expenditure 15(1 + x%) * 60(1 - 20%) = 15 * 60 * (1 - 4%)
15(1 + x%) * 48 = 864
(1 + x%) = 1.2
x% = 0.2
x% = 20%
x = 20

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