`person(1)` sells magazine subscriptions and earns
`$`

for every new subscriber
`P``he(1)` signs up. `person(1)` also earns a
`$`

weekly bonus regardless of how many
magazine subscriptions `Q``he(1)` sells.

If `person(1)` wants to earn at least
`$`

this week, what is the minimum
number of subscriptions `R``he(1)` needs to sell?

To solve this, let's set up an expression to show how much
money `person(1)` will make.

Amount earned this week `=`

`\qquad`

Subscriptions sold
`\times`

Price per subscription
`+`

Weekly bonus

Since `person(1)` wants to make
**at least** `$`

this
week, we can turn this into an inequality.`R`

Amount earned this week
`\geq $`

`R`

Subscriptions sold `\times`

Price per
subscription `+`

Weekly bonus
`\geq $`

`R`

We are solving for the number of subscriptions sold, so let
subscriptions sold be represented by the variable
`x`

.

We can now plug in:

`x \cdot $`

`P` + $`Q` \geq
$`R`

```
x \cdot $
```

`P` \geq
$`R` - $`Q`

```
x \cdot $
```

`P` \geq $`R - Q`

`x \geq \dfrac{`

`R - Q`}{`P`}
\approx `((R - Q) / P).toFixed(2)`

Since `person(1)` cannot sell parts of
subscriptions, we round

up to
`((R - Q) / P).toFixed(2)`

.
`X`

`x \geq \dfrac{`

`R - Q`}{`P`} =
`(R - Q) / P`

`person(1)` must sell at least `X`
subscriptions this week.

For every level `person(1)` completes in
`his(1)` favorite game, `he(1)` earns

points. `P``person(1)` already
has

points in the game and wants to
end up with at least `Q`

points before
`R``he(1)` goes to bed.

What is the minimum number of complete levels that
`person(1)` needs to complete to reach
`his(1)` goal?

To solve this, let's set up an expression to show how many
points `person(1)` will have after each level.

Number of points `=`

`\qquad`

Levels completed
`\times`

Points per level `+`

Starting points

Since `person(1)` wants to have
**at least**

points
before going to bed, we can set up an inequality.
`R`

Number of points `\geq `

`R`

Levels completed `\times`

Points per level
`+`

Starting points ```
\geq
```

`R`

We are solving for the number of levels to be completed, so
let the number of levels be represented by the variable
`x`

.

We can now plug in:

`x \cdot `

`P` + `Q` \geq
`R`

```
x \cdot
```

`P` \geq `R` - `Q`

```
x \cdot
```

`P` \geq `R - Q`

`x \geq \dfrac{`

`R - Q`}{`P`}
\approx `((R - Q) / P).toFixed(2)`

Since `person(1)` won't get points unless
`he(1)` completes the entire level, we round

up to
`((R - Q) / P).toFixed(2)`

.
`X`

`x \geq \dfrac{`

`R - Q`}{`P`} =
`(R - Q) / P`

`person(1)` must complete at least `X`
levels.

To move up to the maestro level in `his(1)` piano
school, `person(1)` needs to master at least

songs. `R``person(1)` has
already mastered

songs.
`Q`

If `person(1)` can typically master

songs per month, what is the minimum
number of months it will take `P``him(1)` to move to the
maestro level?

To solve this, let's set up an expression to show how many
songs `person(1)` will have mastered after each
month.

Number of songs mastered `=`

`\quad`

Months at school
`\times`

Songs mastered per month
`+`

Songs already mastered

Since `person(1)` Needs to have
**at least**

songs
mastered to move to maestro level, we can set up an
inequality to find the number of months needed.
`R`

Number of songs mastered ```
\geq
```

`R`

Months at school `\times`

Songs mastered
per month

`\qquad+`

Songs already mastered
`\geq `

`R`

We are solving for the months spent at school, so let the
number of months be represented by the variable
`x`

.

We can now plug in:

`x \cdot `

`P` + `Q` \geq
`R`

```
x \cdot
```

`P` \geq `R` - `Q`

```
x \cdot
```

`P` \geq `R - Q`

`x \geq \dfrac{`

`R - Q`}{`P`}
\approx `((R - Q) / P).toFixed(2)`

Since we conly care about whole months that
`person(1)` has spent working, we round

up to
`((R - Q) / P).toFixed(2)`

.
`X`

`x \geq \dfrac{`

`R - Q`}{`P`} =
`(R - Q) / P`

`person(1)` must work for at least `X`
months.