Question

Tyler needs at least $205 for a new video game system. He has already saves $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.

Answer 1

Amount needed=earned+already have
205=earned+30
earned=7 times number of hours=7h

205≤7h+30
we used the less than or equal to because he needs at least 205, means 205 or greater must be earned


205≤7h+30
minus 30 both sides
175≤7h
divide both sides by 7
25≤h
needs to work at least 25 hours

Answer 2

So, first, gather your important information:

"at least $205"
"already has $30"
"$7 per hour"

now rewrite this into numbers and symbols:

"at least $205" ... >/= 205 (his money MUST be over 205)
"already has $30" ... +30 (he's already saved 30, so add it)
"$7 per hour" ... 7h (he makes 7 an hour)

put all of those together.
7h + 30 >/= 205

this is your inequality. seven dollars an hour plus the thirty dollars he already saved must equal at least 205.

now, solve it for h:
7h + 30 >/= 205 ... subtract 30
7h >/= 175 ... divide by 7
h >/= 25

because your h variable stands for the hours worked, he must work at least 25 hours to have enough money to buy his new video game system.