Problems from Problems with linear equations

Development:

First we solve the equation: $$x-{\displaystyle \frac{x}{2}}=9\Rightarrow {\displaystyle \frac{2x-2}{2}}=9\Rightarrow {\displaystyle \frac{x}{2}}=9\Rightarrow x=9\cdot 2=18$$

Then, the first statement is direct if it expresses the relation that the equation denotes with words:

If $9$ is subtracted from a number, its half is obtained: what is this number?

An alternative statement might be transforming the number into candies, so that:

How many candies does Irene have if, once she has eaten $9$, she still has half the candies she originally had?

The equation is also valid for this statement since $x-9$ is the amount of candies that she has after eating up $9$ and ${\displaystyle \frac{x}{2}}$ are those that she has left in the end.

Also, an age statement might be written:

How old is Peter if $9$ years ago he was half the age that he is now?

If $x$ is the current age, $x-9$ is the age $9$ years ago, and ${\displaystyle \frac{x}{2}}$ half of its current age, therefore the equation is valid and Peter is $18$ years old.

Solution:

If $9$ is subtracted from a number, its half is obtained: what is this number?

How many candies does Irene have if, once she has eaten $9$, she still has half the candies she had?

How old is Peter if $9$ years ago he was half the age that he is now?

Among many other possibilities.

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