Maths(10 marks)

Question

我有3絛數唔識,唔該教下我(要埋步驟)
1) 3y/2 + p-7y/2 =W
y=?

2) John's saving is$300 more than his sister"s.After giving$450 from his savings to his sister,John becomes 2/5 of his sister's. .How much saving do they have altogether?

3)A car uses 1/4 of its petrol in the first day of a trip, and 1/5 of the rest on the second day.What was the original amount of petrol in the car if there is 6L of petrol left in the tank?

Answer 1

1.
3y/2 + p-7y/2 =W
-4y/2 + p = W
-2y + p = W
-2y = W - p
y = -(W-p) / 2
y = (p - W) / 2

2.
Let $x be John's saving.
Then his sister has $(x-300) saving
After giving $450, John has $(x-450) saving and his sister has $(x-300+450) saving
x-450 = 2/5 * (x-300+450)
x-450 = 2/5 * (x +150)
x - 450 = 2x/5 + 60
x - 2x/5 = 450 + 60
3x/5 = 510
x = 850

Their savings together
= x + (x-300)
= 850 + (850 - 300)
= 1400

Therefore they have $1400 savings together.

3.
Let xL be the original amount of petrol in the car
After 1 day, it had (x - x/4) amount of petrol
After 2 days, it had (x - x/4) - 1/5(x - x/4) amount of petrol

(x - x/4) - 1/5(x - x/4) = 6
3x/4 - 3x/20 = 6
12x / 20 = 6
x =10

Therefore, the car had 10L of petrol

Answer 2

1.

Firstly, the equation multiply 2 => 3y+2p-7y=2w
Then, 2p-4y=2w
Secondly, the equation divide 2 => p-2y=w
After that, => y=(p-w)/2


2. Let’s they have saving altogether be y, sister’s portion is x,

Then John is x+300, they have saving altogether is 2x+300.

x+300-450=2/5(x+450)
x-150=2/5x+180
3/5x=330
x=550

They have saving altogether is 2($550)+$300=$1,400


3. Let’s the original volume be c,

then c*(1-1/4)*(1-1/5)=6 Litre
c=10 Litre

Answer 3

第二題:Let John有$x, sister有$y, 咁要求既答案z=x+y
condition1:John's saving is$300 more than his sister"s
i.e. x=y+300....(1)
condition2:After giving$450 from his savings to his sister,John becomes 2/5 of his sister's
i.e. x-450=2/5(450+y)....(2)
Substitute (1)x=y+300 into (2)
y+300-450=2/5(450+y)
5y+1500-2250=900+2y
3y=1650
y=550
Put y=550 into (1)
x=550+300
x=850
Therefore,z=x+y
=850+550
=1400

第三題:Let the car has xL of petrol originally, and has yL of petrol after first day
condition1:The car uses 1/4 of its petrol in the first day of a trip
i.e. x-1/4x=y
3/4x=y....(1)
condition2:uses 1/5 of the rest on the second day, and have 6L left finally
i.e. y-1/5y=6
4/5y=6....(2)
By solving (2),y=7.5
Put y=7.5 into (1)
3/4x=7.5
x=10
Therefore the original amount of petrol in the car is 10L

第一題好似冇得做啵，又可能係我唸唔到＠＠會唔會打少左野呢？anyway,希望後面兩條唔會寫得太亂啦^^

Answer 4

1)
3y/2 - (p-7y)/2 = w
3y - (p-7y) = 2w
10y = 2w+p
y = (2w+p)/10

2)
Let John and his sister's money be x and y,
x-300 = y ---(1)
(x-450) = (2/5) x (y+450) ---(2)
sub (1) into (2),
5(x-450)=2(x-300+450)
3x=2550
x=850
then, y=550
x+y = 1400

3)
Let the org. volumn be x,
x (1- 3/4) (1- 1/5) = 6
x = 10L

Answer 5

2.3 是英文題目, 因我是讀中文學校, 怕解錯題, 所以只做第一題給你。(注！ 只供參考 )
先全式 x2 = 3y+2p-7y=2w
2p-4y=2w
再全式除2 = p-2y=w
移項整理 = y=(p-w)/2

Answer 6

no know