1. Three boxes A, B and C weigh 12kg altogether. Box A weighs 1.2kg more than B and 0.3kg more than C. What is the weight of the heaviest box?

2. Peter and Ali have 375 cards altogether. If Ali gives 25% of his cards to Peter, he will have 1/4 as many cards as Peter. How many cards does Ali have?

1)

A = B + 1.2
A = C + .3
so,
C = B + .9

so,
A+B+C = B+1.2 + B + B+.9 = 12.0
3B + 2.1 = 12.0
B = 3.3
A = 4.5
C = 4.2

2)
If p a gives 1/4 of his cards to p,

3/4 a = 1/4(p + a/4)
3a = p + a/4
12a = 4p + a
11a = 4p
so,

a + p = a + 11/4 a = 375
15a/4 = 375
15a = 1500
a = 100
so, p = 275

if a gives 25 to p,
then a = 75 and p = 300

this is rubbish dont bother

1. Let's assign variables to the weights of the boxes. Let's say the weight of box B is x kg.

- Box A weighs 1.2kg more than B, so its weight is x + 1.2 kg.
- Box C weighs 0.3kg less than A, so its weight is (x + 1.2) - 0.3 kg = (x + 0.9) kg.

Now let's set up an equation to represent the given condition:
Weight of A + Weight of B + Weight of C = Total weight
(x + 1.2) + x + (x + 0.9) = 12

Combining like terms:
3x + 3.1 = 12

Subtracting 3.1 from both sides:
3x = 8.9

Dividing both sides by 3:
x = 2.9667

Since we can't have a fraction of a kilogram for the weight of the boxes, we can round it to the nearest whole number. Therefore, the weight of box B is approximately 3 kg.

Now let's determine the weight of the other boxes:
- Weight of A = x + 1.2 = 3 + 1.2 = 4.2 kg
- Weight of C = (x + 0.9) = 3 + 0.9 = 3.9 kg

To find the weight of the heaviest box, we compare the weights of A, B, and C. The heaviest weight is 4.2 kg.

Therefore, the weight of the heaviest box is 4.2 kg.

2. Let's assume that Peter has P cards and Ali has A cards.

According to the given condition, Peter and Ali have 375 cards altogether, so we can set up an equation:
P + A = 375

Now let's consider the second condition. If Ali gives 25% of his cards to Peter, he will have 1/4 as many cards as Peter.

If Ali gives 25% of his cards to Peter, he will be left with 75% of his original cards, which is 0.75A.
Since Ali will have 1/4 as many cards as Peter, we can set up another equation:
0.75A = (1/4)P

To solve this system of equations, we can use substitution.

First, let's solve the second equation for P:
P = (4/1) * 0.75A
P = 3A

Now, substitute the value of P in the first equation:
3A + A = 375
4A = 375
A = 375/4
A = 93.75

Since Ali can't have a fraction of a card, we round it to the nearest whole number. Therefore, Ali has approximately 94 cards.

So, Ali has 94 cards.