急!!!今日前!!兩題數學!!THX

1)小明要買入糖果A和B共150KG。在糖果A中，芒果味糖果佔總重量的82%，而在糖果包B中，芒果味的則佔42%。如果他想把全部所買的糖果混合起來，並使芒果味糖果佔總重量的50%，求他須買入每糖果包的重量。

設他買入 (a) kg 糖果包A, (b) kg 糖果包B

a + b = 150..........................................(1)
a x 82% + b x 42% = 150 x 50%...........(2)

From (1),
b = 150 - a...........................................(3)

From (2)
a x 82% + b x 42% = 75........................(4)

Substitute (3) into (4)
a x 82% + ( 150-a ) x 42% = 75
82a + 6300 - 42a = 7500
40a = 1200
a = 30 //

Substitute a = 30 into (3)
b = 150 - 30
b = 120 //

他須買入30kg 糖果包A, 120 kg 糖果包B

2)小明買入一批糖果，蘋果味糖果的價錢為$40/KG，而橙味的則為$60/KG。他將這些糖果混合起來，共重40KG，並全部以$81/KG出售，獲利50%。求他所買每種糖果的重量。

設他買 (a) kg 蘋果味糖果, (b) kg 橙味糖果

a + b = 40...............................................(1)
81(40) = (40a + 60b) x ( 1 + 50% ).............(2)

From (1),
b = 40 - a.................................................(3)

From (2),
(40a + 60b) x ( 1 + 50% ) = 3240 .............(4)

Substitute (3) into (4)
[40a + 60( 40-a )] x ( 1 + 50% ) = 3240
40a + 2400 - 60a = 2160
-20a = -240
a = 12 //

Substitute a = 12 into (3)
b = 40 - 12
b = 28 //

他買 12 kg 蘋果味糖果, 28 kg 橙味糖果

1.
For
A+B = 150,
0.82A + 0.42B = 150 x 0.5 = 75

B = 150 - A
0.82 A + 0.42 ( 150 - A ) = 75

A = 30, B = 120

2.
The cost of the two kinds of sweet is: 81/(1+0.5) x 40 = $2160
For the weight of the apple sweet and orangle sweet are A & O respectively

A + O = 40
40 A + 60 O = 2160
O = 40 - A
40 A + 60 ( 40 - A ) = 2160

A = 12 , O = 28

1). 設他須買入A糖果xKG,則須買入B糖果(150-x)KG

82%x+42%(150-x)=150*50%

0.82x+0.42(150-x)=75

0.82x+63-0.42x=75

0.4x=12

x=30(KG)

...他須買入A糖果30KG,B糖果120KG

2). 設他所買的蘋果味糖果重aKG,則橙味的糖果重(40-a)KG

40a+60(40-a)=81*40*50%

40a+2400-60a=1620

-20a=-780

a=39(KG)

...他所買的蘋果味糖果重39KG,則橙味的糖果重1KG