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

Answer:

#$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.