Write these word problems in mathematical language (without working out the answers): a) the difference between 69 and 43 b) the sum of 112 and 28 c) one third of 24 increased by 8 d) the square root of 16 is equal to the square of 2 e) 15 less than 99 f) 20 more than 16.

$$
d = a + 6 = 6 + 6 = 12
$$
$$
e = b + 6 = 24 + 6 = 30
$$
$$
f = c + 6 = 48 + 6 = 54
$$
The values are: $\boxed{a=6, b=24, c=48, d=12, e=30, f=54}$

• c)

Using the first pair: $1 + g = 22$ $g = 22 - 1$ $g = 21$

$$
16 + 21 = 37
$$
$$
49 + 21 = 70
$$
The value is: $\boxed{g=21}$

3. Write these phrases as expressions (write the unknown number as x):

• a) A number is decreased by the square of 4: $$x - 4^2$$
• b) The product of 6 and a number is increased by 10: $$6x + 10$$
• c) A number divided by 3 is added to the square of that number: $$\frac{x}{3} + x^2$$
• d) A number multiplied by 5 is subtracted from 25: $$25 - 5x$$
• e) Half of a number is added to one third of that number: $$\frac{x}{2} + \frac{x}{3}$$
• f) 2 less than the product of a number and 8: $$8x - 2$$

4. Think of a number. Add 5. Multiply the sum by 2. Subtract 1. Write an expression using $x$ for the unknown. Find the value of this expression if $x = 12.5$.

Let the unknown number be $x$.
Add 5: $x + 5$
Multiply the sum by 2: $2(x + 5)$
Subtract 1: $2(x + 5) - 1$
The expression is: $\boxed{2(x + 5) - 1}$

The value of the expression is: $\boxed{34}$

5. Copy and complete the following table:

For $x = -1$: $3(-1) - 4 = -3 - 4 = -7$
For $x = 0$: $3(0) - 4 = 0 - 4 = -4$
For $x = 3$: $3(3) - 4 = 9 - 4 = 5$
For $x = 10$: $3(10) - 4 = 30 - 4 = 26$

The completed table is:

6. If $a = 2$, $b = 6$ and $c = 5$, find the values of these expressions:

• a) $3b - a$

  $$3(6) - 2 = 18 - 2 = 16$$

  The value is: $\boxed{16}$

• b) $3(b - a)$

  $$3(6 - 2) = 3(4) = 12$$

  The value is: $\boxed{12}$

• c) $a + b - c$

  $$2 + 6 - 5 = 8 - 5 = 3$$

  The value is: $\boxed{3}$

• d) $4b - 2c$

  $$4(6) - 2(5) = 24 - 10 = 14$$

  The value is: $\boxed{14}$

7. Write an expression to describe the relationship of the data in the tables:

• a) Observe the relationship between $m$ and $n$: $7 - 5 = 2$ $10 - 8 = 2$ $14 - 12 = 2$ $19 - 17 = 2$ The output $n$ is always 2 more than the input $m$. The expression is: $\boxed{n = m + 2}$

• b) Observe the relationship between $x$ and $y$: For $x = -1, y = -2 \implies y = 2x$ For $x = -4, y = -8 \implies y = 2x$ For $x = -8, y = -16 \implies y = 2x$ For $x = -16, y = -40 \implies y = 2.5x$ The relationship $y = 2x$ holds for the first three pairs. Assuming there might be a typo in the last value of $y$ (it should be $-32$ for $y=2x$ to hold), the most consistent expression for the majority of the data is: $\boxed{y = 2x}$

8. What number doubled and added to 12 gives 20?

Let the number be $x$.

The number is: $\boxed{4}$