answer:To solve this problem, we need to set up equations based on the information given and then solve for each zone's area.Let's define:- ( A ) as the area of Zone A.- ( B ) as the area of Zone B.- ( C ) as the area of Zone C.We are given the following information:1. The total area is 900 acres: [ A + B + C = 900 ]2. Zone A is twice the size of Zone B: [ A = 2B ]3. Zone C is 100 acres larger than Zone B: [ C = B + 100 ]Now, we have three equations:1. ( A + B + C = 900 )2. ( A = 2B )3. ( C = B + 100 )Substitute equations (2) and (3) into equation (1):[2B + B + (B + 100) = 900]Simplify the equation:[2B + B + B + 100 = 900]Combine like terms:[4B + 100 = 900]Subtract 100 from both sides:[4B = 800]Divide both sides by 4 to solve for ( B ):[B = 200]Now that we have ( B = 200 ), we can find ( A ) and ( C ) using equations (2) and (3):Substitute ( B = 200 ) into equation (2):[A = 2B = 2 times 200 = 400]Substitute ( B = 200 ) into equation (3):[C = B + 100 = 200 + 100 = 300]Therefore, the areas of the zones are:- Zone A: 400 acres- Zone B: 200 acres- Zone C: 300 acres# 400 acres, 200 acres, 300 acres

answer:To solve this problem, we need to determine how many total ambulances are required to meet the city's goal of covering 90 emergencies per day, given that each ambulance can attend to an average of 5 emergencies per day.Step 1: Calculate the total number of ambulances neededThe required number of ambulances can be calculated using the formula:[text{Number of ambulances needed} = frac{text{Total emergencies per day}}{text{Average emergencies per ambulance per day}}]Substitute the given values:[text{Number of ambulances needed} = frac{90}{5} = 18]So, the city needs a total of 18 ambulances to cover 90 emergencies per day.Step 2: Calculate the number of additional ambulances neededThe city currently has 12 ambulances. Therefore, the number of additional ambulances needed is:[text{Additional ambulances needed} = text{Number of ambulances needed} - text{Current number of ambulances}]Substitute the known values:[text{Additional ambulances needed} = 18 - 12 = 6]Therefore, the city needs to purchase 6 additional ambulances.# 6

answer:To find out how many of Soyeon's favorite songs Alex will include in his playlist, we can follow these steps:1. Calculate the Total Number of Songs: - Alex has 8 albums. - Each album has an average of 10 songs. - Therefore, the total number of songs is: [ 8 , text{albums} times 10 , text{songs/album} = 80 , text{songs} ]2. Determine the Number of Favorite Songs: - 15% of these 80 songs are his absolute favorites. - To find the number of favorite songs, calculate 15% of 80: [ 0.15 times 80 = 12 , text{favorite songs} ]Therefore, if Alex includes all of his favorite songs in his playlist, the playlist will have:# 12

answer:To solve this problem, we need to calculate the total time required for the class session based on the given information. Here's the step-by-step solution:1. Time for Each Student to Speak: - Each student is given 5 minutes to speak. - There are 30 students in the class. - Total time for all students to speak = 5 minutes/student × 30 students = 150 minutes.2. Time for Professor Smith to Summarize: - After all students have spoken, Professor Smith will spend 15 minutes summarizing their input.3. Total Time for the Class Session: - Add the time for the students to speak and the time for the professor's summary. - Total class session time = 150 minutes (students) + 15 minutes (summary) = 165 minutes.Final answer:# 165

answer:To find the total amount Mr. Johnson spent on all the plants, we need to calculate the cost for each type of plant separately and then add them together.1. Calculate the total cost for the rose bushes: - Number of rose bushes = 15 - Cost per rose bush = 12 - Total cost for rose bushes = Number of rose bushes × Cost per rose bush [ text{Total cost for rose bushes} = 15 times 12 = 180 ]2. Calculate the total cost for the lavender plants: - Number of lavender plants = 10 - Cost per lavender plant = 8 - Total cost for lavender plants = Number of lavender plants × Cost per lavender plant [ text{Total cost for lavender plants} = 10 times 8 = 80 ]3. Calculate the total cost for the hibiscus plants: - Number of hibiscus plants = 8 - Cost per hibiscus plant = 10 - Total cost for hibiscus plants = Number of hibiscus plants × Cost per hibiscus plant [ text{Total cost for hibiscus plants} = 8 times 10 = 80 ]4. Calculate the total amount spent on all plants: - Total amount spent = Total cost for rose bushes + Total cost for lavender plants + Total cost for hibiscus plants [ text{Total amount spent} = 180 + 80 + 80 = 340 ]Mr. Johnson spent a total of 340 on all the plants for his garden.# 340

answer:Let's break down the problem step by step to find the total cost Alex will incur.1. Initial Purchase: - Alex initially purchases 15 tools. - The price per tool is 75. - Total cost for the initial purchase: [ 15 times 75 = 1125 text{ dollars} ]2. Additional Purchase: - Alex decides to double the facility's inventory. Therefore, he needs to purchase an additional 15 tools (since he already has 15, doubling means having 30 in total). - The additional purchase will be for 15 more tools. - The total number of tools after this purchase will be 30.3. Discount: - Since the total number of tools after the additional purchase exceeds 20, Alex qualifies for a 10% discount on the additional purchase. - The cost of the additional 15 tools without discount: [ 15 times 75 = 1125 text{ dollars} ] - The discount is 10% of the additional purchase cost: [ text{Discount} = 1125 times frac{10}{100} = 112.5 text{ dollars} ] - The cost after applying the discount: [ 1125 - 112.5 = 1012.5 text{ dollars} ]4. Total Cost: - The total cost Alex incurs is the sum of the initial purchase cost and the discounted cost of the additional purchase: [ text{Total Cost} = 1125 + 1012.5 = 2137.5 text{ dollars} ]# 2137.5