Kris currently has $190 and plans to earn more money each of the 8 weekends this summer. She wants at least $1,625 by the end of the summer. Write and solve an inequality for the amount of money Kris needs to earn each weekend. Which answer choice best interprets the solution in the context of the problem?(1 point)

Responses

Kris needs to earn $13.13 each hour to meet her goal.
Kris needs to earn $13.13 each hour to meet her goal.

Kris needs to earn at least $179.38 each weekend to meet her goal.
Kris needs to earn at least $179.38 each weekend to meet her goal.

Kris needs to earn $105 more to meet her goal.
Kris needs to earn $105 more to meet her goal.

Kris needs $179.38 more to meet her goal.

1 answer

To solve this problem, we start by determining how much more money Kris needs to earn to reach her goal of at least $1,625 by the end of summer.

  1. Calculate how much more Kris needs: \[ 1625 - 190 = 1435 \] So, Kris needs to earn at least $1,435 more.

  2. Let \( x \) be the amount of money Kris needs to earn each weekend. Since she wants to earn this amount over 8 weekends, we can write the inequality: \[ 8x \geq 1435 \]

  3. To find \( x \), divide both sides of the inequality by 8: \[ x \geq \frac{1435}{8} \] \[ x \geq 179.375 \]

  4. Rounding this to two decimal places, we get: \[ x \geq 179.38 \]

Thus, Kris needs to earn at least $179.38 each weekend to meet her goal.

Now, we'll consider the response options:

  • Kris needs to earn $13.13 each hour to meet her goal. (This choice is incorrect as the earning calculation is per weekend, not per hour.)
  • Kris needs to earn at least $179.38 each weekend to meet her goal. (This choice is correct.)
  • Kris needs to earn $105 more to meet her goal. (This choice is incorrect as she needs to earn $1435 more.)
  • Kris needs $179.38 more to meet her goal. (This choice is incorrect, she needs to earn that amount each weekend, not an additional amount.)

The best interpretation of the solution is: Kris needs to earn at least $179.38 each weekend to meet her goal.