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?

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Answer 1 · 2017-08-06T00:24:59

$$55 + $9 x ge $199$

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

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.