Question

You have already saved $55. You earn $9 per hour at your job. You are saving for a bicycle that costs $199. How do you write an inequality that represents the possible numbers of hours you need to work to buy the bicycle?

Answer 1

`$55 + $9 x ge $199`

You must work for at least `16` hours to be able to buy the bicycle.

Explanation:

Let `x` represent the number of hours you need to work to buy the bicycle.

You already have `$55`.

`Rightarrow $55 + underline(" " " ") ge underline(" " " ")`

You also earn `$9` per hour.

Algebraically, this can be written as `9 x`.

`Rightarrow $55 + $9 x ge underline(" " " ")`

You need to earn at least `$199` to buy the bicycle.

`Rightarrow $55 + $9 x ge $199`

The `ge` sign is used because the left-hand side of the inequality must be "greater than or equal to" `$199`.

Let's find out how many hours you need to work to buy the bicycle.

Subtracting `$55` from both sides of the inequality:

`Rightarrow $55 - $55 + 9 x ge $199 - $55`

`Rightarrow $9 x ge $144`

Dividing both sides by `$9`:

`Rightarrow frac($9 x)($9$) = frac($144)($9)`

`therefore x ge 16`

Therefore, you need to work at least `16` hours to afford the bicycle.