Maeve currently has $130 and plans to earn more money each of the 8 weekends this summer. She wants at least $1,250 by the end of the summer. How much does she need to earn each weekend? Assume she earns the same amount each weekend. Solve her problem, and then graph the solution on a number line.(1 point)
Responses
An illustration shows a number line labeled Maeve's Earnings. The number line ranges from 0 to 90 in 10 unit increments. A closed point is plotted at 10. An arrow extends from that point to the right and goes beyond 90.
Image with alt text: An illustration shows a number line labeled Maeve's Earnings. The number line ranges from 0 to 90 in 10 unit increments. A closed point is plotted at 10. An arrow extends from that point to the right and goes beyond 90.
An illustration shows a number line labeled Maeve’s Earnings This Summer. The number line ranges from 0 to 180 in 20 unit increments. A closed point is plotted at 140. An arrow extends from that point to the right and goes beyond 180.
Image with alt text: An illustration shows a number line labeled Maeve’s Earnings This Summer. The number line ranges from 0 to 180 in 20 unit increments. A closed point is plotted at 140. An arrow extends from that point to the right and goes beyond 180.
An illustration shows a number line labeled Maeve's Earnings Each Weekend. The number line ranges from 0 to 180 in 20 unit increments. A closed point is plotted at 140. An arrow extends from that point to the right and goes beyond 180.
Image with alt text: An illustration shows a number line labeled Maeve's Earnings Each Weekend. The number line ranges from 0 to 180 in 20 unit increments. A closed point is plotted at 140. An arrow extends from that point to the right and goes beyond 180.
An illustration shows a number line labeled Maeve’s Earnings Each Weekend. The number line ranges from 0 to 2,000 in 500 unit increments. A closed point is plotted at 1,250. An arrow extends from that point to the right and goes beyond 2,000.
Image with alt text: An illustration shows a number line labeled Maeve’s Earnings Each Weekend. The number line ranges from 0 to 2,000 in 500 unit increments. A closed point is plotted at 1,250. An arrow extends from that point to the right and goes beyond 2,000.
An illustration shows a number line labeled Maeve’s Earnings Each Weekend. The number line ranges from 0 to 2,000 in 500 unit increments. A closed point is plotted at 1,250. An arrow extends from that point to the right and goes beyond 2,000.
Lionel is loading boxes of books into an elevator to move to the 35th floor of an office building. There are 10 boxes of books, and Lionel wants to make sure he is not exceeding the maximum weight of the elevator, which is 2,000 pounds. Lionel weighs 170 pounds. If each box of books weighs the same amount, how much can each box weigh? Solve this problem and then graph the solution on a number line.(1 point)
To find out how much each box can weigh, we can subtract Lionel's weight from the maximum weight of the elevator and then divide the result by the number of boxes.
Maximum weight of elevator = 2000 pounds
Lionel's weight = 170 pounds
Number of boxes = 10
Weight each box can weigh = (Maximum weight of elevator - Lionel's weight) / Number of boxes
Weight each box can weigh = (2000 - 170) / 10
Weight each box can weigh = 1830 / 10
Weight each box can weigh = 183 pounds
Therefore, each box of books can weigh 183 pounds.
Now, let's graph the solution on a number line.
An illustration shows a number line labeled Box Weight. The number line ranges from 0 to 200 in 20 unit increments. A closed point is plotted at 183. An arrow extends from that point to the right and goes beyond 200.
Image with alt text: An illustration shows a number line labeled Box Weight. The number line ranges from 0 to 200 in 20 unit increments. A closed point is plotted at 183. An arrow extends from that point to the right and goes beyond 200.
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 $179.38 more to meet her goal.
Kris needs $179.38 more 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 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.
To find the amount of money Kris needs to earn each weekend, we can subtract her current savings from her goal savings and then divide the result by the number of weekends.
Current savings = $190
Goal savings = $1,625
Number of weekends = 8
Money Kris needs to earn each weekend = (Goal savings - Current savings) / Number of weekends
Money Kris needs to earn each weekend = ($1,625 - $190) / 8
Money Kris needs to earn each weekend = $1,435 / 8
Money Kris needs to earn each weekend = $179.38
Therefore, the solution is that Kris needs to earn at least $179.38 each weekend to meet her goal.
The best answer choice that interprets the solution in the context of the problem is:
Kris needs to earn at least $179.38 each weekend to meet her goal.
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)
Responses
Jada needs to do at least 14 push-ups each day for the rest of the week to meet her goal.
Jada needs to do at least 14 push-ups each day for the rest of the week to meet her goal.
Jada needs to do push-ups for at least 12 more days to meet her goal.
Jada needs to do push-ups for at least 12 more days to meet her goal.
Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal.
Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal.
Jada needs to do at least 10 push-ups each day for the rest of the week to meet her goal.
To find the number of push-ups Jada needs to do each day for the rest of the week to meet her goal, we can subtract the number of push-ups she has already done from her goal and then divide the result by the number of remaining days in the week.
Goal number of push-ups = 100
Number of push-ups Jada has already done = 30
Number of remaining days in the week = 7 - 1 = 6 (since Jada already did push-ups on Sunday)
Number of push-ups Jada needs to do each day = (Goal number of push-ups - Number of push-ups Jada has already done) / Number of remaining days in the week
Number of push-ups Jada needs to do each day = (100 - 30) / 6
Number of push-ups Jada needs to do each day = 70 / 6
Number of push-ups Jada needs to do each day ≈ 11.67
Since Jada wants to do the same number of push-ups each day for the rest of the week, we can round up to the nearest whole number to ensure she meets her 100 push-up goal. Therefore, the solution is that Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal.
The best answer choice that interprets the solution in the context of the problem is:
Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal.
Teddy is solving the following problem: James earns $400 a week plus $5 in tips for each customer he serves. He is hoping to earn more than $1,000 this week. How many customers would he have to serve to meet his goal? Describe the solutions. Teddy writes the inequality 5x+400>1,000 , where x is the number of customers James serves. Teddy solves the inequality and finds that x>120 . How should Teddy interpret this solution in the context of the problem?(1 point)
Responses
James needs to earn at least $120 each day this week to meet his goal.
James needs to earn at least $120 each day this week to meet his goal.
James needs to serve more than 120 customers this week to meet his goal.
James needs to serve more than 120 customers this week to meet his goal.
James needs to serve at least 120 customers this week to meet his goal.
James needs to serve at least 120 customers this week to meet his goal.
James needs to earn more than $120 each day this week to meet his goal.
Teddy should interpret the solution, x > 120, in the context of the problem as:
James needs to serve more than 120 customers this week to meet his goal.
The inequality 5x + 400 > 1,000 means that the total earnings from $5 tips per customer, represented by 5x, plus the base salary of $400, should be greater than $1,000 in order for James to earn more than $1,000 in total. When Teddy solves the inequality, he finds that x > 120, which means that the number of customers James serves should be greater than 120 for him to meet his goal of earning more than $1,000.
Therefore, Teddy should interpret the solution as James needing to serve more than 120 customers this week to meet his goal.