Let's use inequalities to compare the number of weeks Katie and Rebecca will need to reach their goals.
Let x be the number of weeks Katie needs, and y be the number of weeks Rebecca needs.
For Katie:
$525 + 25x \geq $1250
25x \geq $1250 - $525
25x \geq $725
x \geq 29
For Rebecca:
$510 + 30y \geq $1350
30y \geq $1350 - $510
30y \geq $840
y \geq 28
Therefore, Katie will need at least 29 weeks to reach her goal, while Rebecca will need at least 28 weeks. We can graph this inequality on a number line to visualize the possible number of weeks they will need:
[ 28 ------•-------------- 29 ------•------------- ]
So, Rebecca will need more weeks to reach her goal to participate in her sports activity compared to Katie.
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.
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