Evaluate the given number sentences for truthfulness and solve for the unknown variable in the others.

$$36 = 36$$

The statement is true.

b)

$$36 \neq 72$$

The statement is false.

2. Find the numbers that make the number sentences true.

a) Let the missing number be $x$.

$$15x - 11x - 11 = 1$$ $$4x - 11 = 1$$

$$4x = 1 + 11$$ $$4x = 12$$

$$x = \frac{12}{4}$$ $$x = 3$$

The number is $\boxed{3}$.

b) Let the missing number be $x$.

$$100 = 3x + 5x - 28$$ $$100 = 8x - 28$$

$$100 + 28 = 8x$$ $$128 = 8x$$

$$x = \frac{128}{8}$$ $$x = 16$$

The number is $\boxed{16}$.

c) Let the missing number be $x$.

$$1500 = 20x - 10x + 1250$$ $$1500 = 10x + 1250$$

$$1500 - 1250 = 10x$$ $$250 = 10x$$

$$x = \frac{250}{10}$$ $$x = 25$$

The number is $\boxed{25}$.

3. A factory worker is bored with his job, so he decides to make it more interesting while filling his 30 bottles of cordial. He decides to put the lid on every fourth bottle, the flavour in every fifth bottle and the label on every sixth bottle. If he started at the 1st bottle, how many bottles would have:

Total bottles = 30.
Lids on multiples of 4: $\{4, 8, 12, 16, 20, 24, 28\}$
Flavour in multiples of 5: $\{5, 10, 15, 20, 25, 30\}$
Label on multiples of 6: $\{6, 12, 18, 24, 30\}$

a) Lids on?

$$4, 8, 12, 16, 20, 24, 28$$

There are 7 such bottles.
The number of bottles with lids is $\boxed{7}$.

b) Lids and flavours?

This means multiples of LCM(4, 5).

$$LCM(4, 5) = 20$$

$$20$$

There is 1 such bottle.
The number of bottles with lids and flavours is $\boxed{1}$.

c) Flavours and labels?

This means multiples of LCM(5, 6).

$$LCM(5, 6) = 30$$

$$30$$

There is 1 such bottle.
The number of bottles with flavours and labels is $\boxed{1}$.

d) Lids, flavours and labels?

This means multiples of LCM(4, 5, 6).

$$LCM(4, 5, 6) = LCM(2^2, 5, 2 \times 3) = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60$$

There are no multiples of 60 within the first 30 bottles.
The number of bottles with lids, flavours, and labels is $\boxed{0}$.

4. Solve the following order of operation sums:

a)

$$7 \times 5 = 35$$

The answer is $\boxed{35}$.

b)

$$18 \div 9 = 2$$

The answer is $\boxed{2}$.

c)

$$15 + 30 = 45$$

The answer is $\boxed{45}$.

d)

$$25 \times 3 = 75$$

The answer is $\boxed{75}$.

e)

$$21 - 5 + 42 = 16 + 42$$ $$16 + 42 = 58$$

The answer is $\boxed{58}$.

f)