10. A number increased by 7.9 is 8.3 . 12. The quotient of a number and 8 is 4 . 14. The difference between 31 and a number is 7 .

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To solve these problems, we will set up equations based on the given information and then solve for the unknown numbers.

1. A number increased by 7.9 is 8.3:
Let the number be $$ x $$.
The equation based on the given information is:
$$ x + 7.9 = 8.3 $$

2. The quotient of a number and 8 is 4:
Let the number be $$ y $$.
The equation based on the given information is:
$$ \frac{y}{8} = 4 $$

3. The difference between 31 and a number is 7:
Let the number be $$ z $$.
The equation based on the given information is:
$$ 31 - z = 7 $$

Now, we will solve each equation to find the unknown numbers.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x+7.9=8.3$$
- step1: Move the constant to the right side:
  $$x=8.3-7.9$$
- step2: Subtract the numbers:
  $$x=0.4$$
Solving the first equation $$ x + 7.9 = 8.3 $$ gives us:
$$ x = 0.4 $$

2. Solving the second equation $$ \frac{y}{8} = 4 $$ gives us:
$$ y = 32 $$

3. Solving the third equation $$ 31 - z = 7 $$ gives us:
$$ z = 24 $$

Therefore, the unknown numbers are:
1. $$ x = 0.4 $$
2. $$ y = 32 $$
3. $$ z = 24 $$
The unknown numbers are: 1. 0.4 2. 32 3. 24

A number increased by
7.9 is 8.3 .

The quotient of a number
and 8 is 4 .

The difference between 31 and a
number is 7 .

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A number increased by 7.9 is 8.3 . The quotient of a number and 8 is 4 . The difference between 31 and a number is 7 .