Katie and Rebecca are each trying to earn money to pay for their sports activities for next year.
To help Katie earn money, her parents told her she could walk the dog every day of the week. Katie has $525 already saved. She earns $25 per week walking the dog. Her goal is to have $1250 to play on the soccer team.
To help Rebecca earn money, her parents told her she could do the dishes each night of the week. Rebecca has $510 already saved. She earns $30 per week washing dishes. Her goal is to have $1350 to play on the hockey team.
Determine whether Katie or Rebecca will need more weeks to reach their goal to participate in their sports activities. Use an inequality to graph the possible number of weeks that person will need in order to reach their goal.
Let x be the number of weeks needed to reach their goal.
For Katie:
Total amount needed = $1250
Total amount saved + Total earnings = $525 + $25x
So, inequality is:
$525 + $25x ≥ $1250
$25x ≥ $725
x ≥ 29
For Rebecca:
Total amount needed = $1350
Total amount saved + Total earnings = $510 + $30x
So, the inequality is:
$510 + $30x ≥ $1350
$30x ≥ $840
x ≥ 28
Therefore, Katie will need more weeks to reach their goal compared to Rebecca.
The graph for Katie's inequality is x ≥ 29 and for Rebecca's inequality is x ≥ 28.