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question:Jamie is a benefits analyst who is helping employees choose the best retirement plans. She needs to present data about two different options: Plan A and Plan B. Plan A requires an employee to contribute 150 per month and the employer matches 50% of the employee's contribution. Plan B requires an employee to contribute 200 per month, and the employer matches 25% of the employee's contribution. Jamie has an employee, Alex, who wants to know how much total contribution (employee's contribution plus employer's match) will be accumulated in one year for each plan. Calculate the total contribution for both Plan A and Plan B for Alex over the course of one year (12 months).
answer:To solve the problem, let's calculate the total contribution for both Plan A and Plan B over the course of one year (12 months). Plan A:1. Employee's Contribution: - Alex contributes 150 per month. - For 12 months, the contribution is: [ 150 , text{dollars/month} times 12 , text{months} = 1800 , text{dollars} ]2. Employer's Match: - The employer matches 50% of the employee's contribution. - Monthly employer match: [ 0.50 times 150 , text{dollars} = 75 , text{dollars/month} ] - For 12 months, the employer's match is: [ 75 , text{dollars/month} times 12 , text{months} = 900 , text{dollars} ]3. Total Contribution for Plan A: - Total contribution is the sum of the employee's contribution and the employer's match: [ 1800 , text{dollars} + 900 , text{dollars} = 2700 , text{dollars} ]Plan B:1. Employee's Contribution: - Alex contributes 200 per month. - For 12 months, the contribution is: [ 200 , text{dollars/month} times 12 , text{months} = 2400 , text{dollars} ]2. Employer's Match: - The employer matches 25% of the employee's contribution. - Monthly employer match: [ 0.25 times 200 , text{dollars} = 50 , text{dollars/month} ] - For 12 months, the employer's match is: [ 50 , text{dollars/month} times 12 , text{months} = 600 , text{dollars} ]3. Total Contribution for Plan B: - Total contribution is the sum of the employee's contribution and the employer's match: [ 2400 , text{dollars} + 600 , text{dollars} = 3000 , text{dollars} ]Now, we can summarize the total contributions for both plans:- Plan A: 2700- Plan B: 3000# 2700 dollars for Plan A and 3000 dollars for Plan B
question:Jamie, a nature enthusiast, embarks on a hiking adventure through the forest. On the first day, they hike 8 miles and set up camp. The next day, Jamie hikes 3 miles further into the forest to reach a beautiful waterfall, where they spend the day observing the wildlife. On the third day, Jamie decides to hike 2 miles to explore a hidden grove they heard about from another hiker. After enjoying the serene spot, they hike 5 miles back towards the trailhead. How many total miles did Jamie hike over these three days?
answer:To determine the total distance Jamie hiked over the three days, we can break down the problem and add up the miles hiked each day:Day 1:- Jamie hikes 8 miles and sets up camp.- Total for Day 1 = 8 miles.Day 2:- Jamie hikes an additional 3 miles to reach the waterfall.- Total for Day 2 = 3 miles.Day 3:- Jamie hikes 2 miles to explore the hidden grove.- Then, Jamie hikes 5 miles back towards the trailhead.- Total for Day 3 = 2 miles + 5 miles = 7 miles.Now, let's add up the total miles Jamie hiked over the three days:[text{Total miles} = text{Day 1 miles} + text{Day 2 miles} + text{Day 3 miles}][text{Total miles} = 8 + 3 + 7 = 18 text{ miles}]Thus, the total number of miles Jamie hiked over the three days is 18 miles.# 18
question:A researcher is working with a collector to authenticate and uncover the origins of newly acquired weapons. They recently acquired a batch of 30 ancient swords. To authenticate them, the researcher performs a series of tests, each taking 15 minutes per sword. However, 5 of the swords require additional testing, which takes an extra 10 minutes per sword. If the researcher works for 6 hours a day, how many days will it take to complete the testing of all the swords?
answer:To solve this problem, we need to calculate the total time required to test all the swords and then determine how many days it will take given the researcher's daily working hours. Step-by-Step Solution1. Determine the time required for the initial tests: - Each sword takes 15 minutes for the initial test. - There are 30 swords, so the total time for initial testing is: [ 30 text{ swords} times 15 text{ minutes/sword} = 450 text{ minutes} ]2. Determine the additional testing time for the specific swords: - 5 swords require an additional 10 minutes each. - Total extra time for these 5 swords is: [ 5 text{ swords} times 10 text{ minutes/sword} = 50 text{ minutes} ]3. Calculate the total testing time: - Add the initial testing time and the additional testing time: [ 450 text{ minutes} + 50 text{ minutes} = 500 text{ minutes} ]4. Convert the total time from minutes to hours: - There are 60 minutes in an hour, so: [ 500 text{ minutes} div 60 text{ minutes/hour} = frac{500}{60} approx 8.33 text{ hours} ]5. Determine the number of days required: - The researcher works 6 hours per day. - Divide the total hours by the number of hours per day: [ frac{8.33 text{ hours}}{6 text{ hours/day}} approx 1.39 text{ days} ] - Since the researcher cannot work a fraction of a day, they will need to round up to the next whole number of days.Therefore, it will take 2 days to complete the testing of all the swords.# 2
question:Sarah is a pregnant woman who has been diagnosed with gestational diabetes. Her doctor advises her to monitor her carbohydrate intake closely. For breakfast, Sarah plans to consume a meal consisting of oatmeal, a banana, and a glass of milk. The oatmeal contains 30 grams of carbohydrates, the banana has 27 grams, and the glass of milk adds another 12 grams of carbohydrates. Sarah's dietitian recommends she limit her breakfast to a maximum of 60 grams of carbohydrates to manage her blood sugar levels.How many grams of carbohydrates does Sarah's planned breakfast exceed her recommended limit by, if at all?
answer:To solve the problem, we need to calculate the total amount of carbohydrates in Sarah's planned breakfast and compare it to the recommended limit of 60 grams.Step 1: Calculate the total carbohydrates in the planned breakfast.- Oatmeal: 30 grams- Banana: 27 grams- Milk: 12 gramsTotal carbohydrates = 30 grams (oatmeal) + 27 grams (banana) + 12 grams (milk)Step 2: Add the carbohydrates together.Total carbohydrates = 30 + 27 + 12 = 69 gramsStep 3: Determine how many grams this exceeds the recommended limit of 60 grams.Excess carbohydrates = Total carbohydrates - Recommended limitExcess carbohydrates = 69 grams - 60 gramsExcess carbohydrates = 9 gramsSarah's planned breakfast exceeds her recommended limit by 9 grams.# 9 grams
question:Tom is a loyal New England Patriots fan who loves to watch every game with his friends. After a tough season, Tom decides to cheer up the team with some encouraging messages. He sends 5 messages to each of his favorite 4 players. If he also sends an additional 3 messages to the coach, how many messages in total does Tom send?
answer:To solve the problem, we need to calculate the total number of messages Tom sends, considering both the players and the coach.1. Messages sent to players: - Tom sends 5 messages to each of his 4 favorite players. - To find the total messages sent to players, we multiply the number of messages per player by the number of players: [ 5 , text{messages/player} times 4 , text{players} = 20 , text{messages} ]2. Messages sent to the coach: - Tom sends an additional 3 messages to the coach.3. Total messages sent: - To find the total number of messages sent by Tom, we add the messages sent to the players and the messages sent to the coach: [ 20 , text{messages} + 3 , text{messages} = 23 , text{messages} ]Thus, the total number of messages Tom sends is 23.# 23
question:Alex is a PhD student studying criminology and is conducting a research project analyzing the time it takes for different types of cases to be resolved in a local court. Alex collected data on 5 criminal cases and 3 civil cases. On average, each criminal case took 8 months to resolve, and each civil case took 5 months to resolve. How many total months did it take to resolve all the cases Alex studied?
answer:To solve the problem, we need to calculate the total time it took to resolve all the criminal cases and all the civil cases separately, and then add these two totals together.Step 1: Calculate the total time for the criminal cases.- We know there are 5 criminal cases.- On average, each criminal case took 8 months to resolve.- Therefore, the total time for the criminal cases is calculated as: [ text{Total time for criminal cases} = 5 text{ cases} times 8 text{ months/case} = 40 text{ months} ]Step 2: Calculate the total time for the civil cases.- We know there are 3 civil cases.- On average, each civil case took 5 months to resolve.- Therefore, the total time for the civil cases is calculated as: [ text{Total time for civil cases} = 3 text{ cases} times 5 text{ months/case} = 15 text{ months} ]Step 3: Calculate the total time for all cases.- Add the total time for the criminal cases and the total time for the civil cases: [ text{Total time for all cases} = 40 text{ months} + 15 text{ months} = 55 text{ months} ]# 55