Tyler needs at least $205 for a new video game system. He has already saved $30. He earns $7 an hour at his job. Write and solve an inequality to find how many hours he will need to work to buy the system. Interpret the solution._?

Question

Eli Assouline · Accepted Answer

Tyler needs to work at least 25 hours

The words "at least" indicate that an "inequality" is needed here to describe Tyler's situation. let's use the letter #T# (Target) to represent the amount of money that Tyler needs, #x# for the amount of money he has and #h# for the number of hours he works. things we are told: #T >= 205# #x = 30 + 7h# If he reaches his target then # x = T# so: # 30 + 7h >= 205# subtract 30 from both sides # 7h >= 203 - 30# # 7h >=175# divide both sides by 7 #h >= 25#

Hazel Anglin · Answer

undefined Let $ h $ represent the number of hours Tyler needs to work to buy the video game system. The total amount he will have after working $ h $ hours is $ 7h $ (since he earns $7 per hour). Adding the amount he has already saved ($30) to the amount he earns gives the total amount of money Tyler will have.

We want this total amount to be at least $205, so we can write the following inequality:

$$ 7h + 30 \geq 205 $$

To solve for $ h $, we can subtract 30 from both sides and then divide by 7:

$$ 7h \geq 175 $$

$$ h \geq \frac{175}{7} $$

$$ h \geq 25 $$

Tyler needs to work at least 25 hours to buy the video game system.

Interpretation: Tyler needs to work for at least 25 hours at his job to have enough money to buy the video game system, given that he has already saved $30 and earns $7 per hour.