# 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? ##### 1 Answer Aug 6, 2017 $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.