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)
Let's denote the amount of money Kris needs to earn each weekend by x.
According to the problem, Kris plans to earn money each of the 8 weekends this summer. So, the total amount of money she will earn over the 8 weekends is 8x.
Furthermore, it is given that Kris currently has $190. Therefore, the total amount of money Kris will have by the end of the summer is 190 + 8x.
According to the problem, Kris wants at least $1,625 by the end of the summer. Therefore, we can create the inequality:
190 + 8x ≥ 1625
Now, let's solve this inequality for x:
8x ≥ 1435
x ≥ 179.375
The solution to the inequality is x ≥ 179.375, which means that Kris needs to earn at least $179.375 each weekend.
Interpretation: Kris needs to earn at least $179.375 each weekend in order to have at least $1,625 by the end of the summer.
Jada has challenged herself to do at least 100 full push-ups this week. On Sunday, she does 30 push-ups. Her arms are sore, so she decides to do fewer push-ups on the remaining days of the week. She wants to do the same number of push-ups each day for the rest of the week. Write and solve an inequality for the number of push-ups Jada needs to do each day for the rest of the week to meet her goal of 100 push-ups. Which answer choice best interprets the solution in the context of the problem?(1 point)
Let's denote the number of push-ups Jada needs to do each day for the rest of the week by x.
According to the problem, Jada has already done 30 push-ups on Sunday. So, the total number of push-ups she needs to do for the rest of the week is 100 - 30 = 70 push-ups.
Furthermore, Jada wants to do the same number of push-ups each day for the rest of the week. Therefore, the total number of push-ups she will do for the rest of the week is (the number of remaining days) * x.
According to the problem, Jada wants to do at least 100 push-ups in total for the week. Therefore, we can create the inequality:
70 ≤ (the number of remaining days) * x
Now, let's solve this inequality for x:
70 ≤ (7 - 1) * x
70 ≤ 6x
x ≥ 70/6
x ≥ 11.6667
The solution to the inequality is x ≥ 11.6667, which means that Jada needs to do at least 11.6667 push-ups each day for the rest of the week to meet her goal of 100 push-ups.
Interpretation: Jada needs to do at least 11.6667 push-ups each day for the rest of the week in order to meet her goal of 100 push-ups. Since Jada cannot do a fraction of a push-up, she should aim to do at least 12 push-ups each day.
To answer this question, we need to consider the total amount of money Kris needs to earn each weekend in order to reach or exceed $1,625 by the end of the summer.
Let's denote the amount of money Kris needs to earn each weekend as "x".
Since there are 8 weekends in the summer, Kris plans to earn money for 8 weekends. The total amount of money she will earn can be calculated by multiplying the amount earned each weekend (x) by the number of weekends (8):
Total amount earned = x * 8
We are given that Kris currently has $190, so the equation becomes:
190 + x * 8 ≥ 1625
Now, to solve this inequality, we will subtract 190 from both sides of the equation:
x * 8 ≥ 1435
Finally, to isolate x, we will divide both sides of the equation by 8:
x ≥ 179.375
So, the inequality for the amount of money Kris needs to earn each weekend is x ≥ 179.375.
Now, let's interpret the solution in the context of the problem. Since the amount of money Kris needs to earn is in dollars, we round up the solution to the nearest dollar. Therefore, Kris needs to earn at least $180 each weekend in order to reach or exceed $1,625 by the end of the summer.
The best answer choice that interprets the solution in the context of the problem would be: "Kris needs to earn at least $180 each weekend to meet her goal of having $1,625 by the end of the summer."