教下我幾題Maths吖!!

1)The sum of two numbers, A and B, is 33. If 3/5 of A is equal to one half of B, find the two numbers.
Let the number of A be x.
The number of B = 33 –x
3/5 x = (33-x)/2
Multiply both sides by 2
2(3/5)x = 33 – x
6/5 x = 33 – x
Multiply both sides by 5
5(6/5)x = 33(5) – 5x
6x = 165 – 5x
6x + 5x = 165
11x = 165
x = 165/11
x = 15
B = 33 –x
B = 33 -15
B = 18
A = 15

2)Vincent ,Mary and Minnie buy a $284 gift to their father and they share the payment.
Vincent's share is 5 times Minnie's, while Mary's share is 2 times Minnie's. Find MIinnie's share.
Let x be the MIinnie's share
Vincent's share 5x
Mary's share 2x
All three x + 5x + 2x = $284
8x = $284
x = $284/8
x = $35.50

MIinnie's share is $35.50

3)The weight of a cat is 0.3 kg more than 12 times that of a rat,while the weight of a dog
is 0.2 kg less that 14 times that of the rat. If the weights of the cat and the dog are the same,
(a) what weight in kg is the rat?
(b) what weight in kg is the cat?

Let x be the weight of rat
Weight of cat = 12x + 0.3
Weight of dog = 14x – 0.2
Weight of cat = Weight of dog
12x + 0.3 = 14x – 0.2
0.3 + 0.2 = 14x – 12x
0.5 = 2x
x = 0.5/2 = 0.25 kg
Weight of cat = 12x + 0.3 = 12(0.25) + 0.3 = 3 + 0.3 = 3.3 kg

(a) Weight of the rat is 0.25 kg
(b) Weight of the cat is 3.3 kg

1)
Let number of A be x, number of B be (33-x)
3/5x=1/2 (33-x)
3/5x=33/2-1/2x
3/5x+1/2x=33/2
1.1x=16.5
x=15
∴number of A be 15, number of B be (33-15)=18