Katie's volleyball team is raising funds to purchase personalized team duffle bags for each member on the team. The goal is to raise at least $500. They have currently raised $136 towards their goal. Team members are asked to write and solve an inequality to show how much money is still needed in order to reach their goal.
The members of the team have written the following inequalities and solutions.
Team Members
1 x − 136 > 500; x > 364
The team still needs to raise more than $364.
2 x + 136 > 500; x > 636
The team still needs to raise more than $636.
3 x + 136 > 500; x >364
The team still needs to raise more than $364.
4 x − 136 > 500; x > 636
The team still needs to raise more than $636.
Which team members answered incorrectly? Why are they wrong?
Team members 2 and 4 answered incorrectly. They incorrectly added or subtracted $136 to the amount needed to reach the goal. This mistake led to incorrect solutions. The correct way to set up the inequality is to subtract the amount raised ($136) from the goal amount ($500) and then solve for x.
So the correct way to set up the inequality is:
1 x - 136 < 500
x < 636
This means that the team still needs to raise less than $636 in order to reach their goal.