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question:Samantha, a single mother who loves durable wooden toys, has a collection that she shares with her friend Lisa, another young single mother. Samantha has 15 wooden toys and Lisa has 10 wooden toys. They decide to combine their collections to create a shared play area for their children. After combining their toys, they realize that 5 of the toys are identical, so they decide to donate these to a local daycare. How many unique wooden toys do Samantha and Lisa have left in their shared collection after the donation?
answer:To solve this problem, we need to determine the number of unique wooden toys remaining in the shared collection after the donation of identical toys. Here's the step-by-step breakdown:1. Combine Samantha's and Lisa's Toy Collections: Samantha has 15 wooden toys, and Lisa has 10 wooden toys. Combined, they have: [ 15 + 10 = 25 text{ toys} ]2. Identify and Remove Identical Toys: They realize that 5 of these toys are identical. Since these toys are identical, they are not considered unique in the context of this problem.3. Donate Identical Toys: They decide to donate these 5 identical toys to a local daycare. After donating, these toys are no longer in their shared collection.4. Calculate Remaining Unique Toys: Initially, they had 25 toys in total. Removing the 5 identical toys leaves them with: [ 25 - 5 = 20 text{ unique toys} ]Therefore, after donating the identical toys, Samantha and Lisa have 20 unique wooden toys left in their shared collection.# 20
question:Mrs. Thompson, a retired school teacher, loves spending her days in the peaceful countryside tending to her small vegetable garden. She has planted 24 tomato plants and 18 cucumber plants in her garden. Each tomato plant produces 8 tomatoes, and each cucumber plant yields 5 cucumbers. Mrs. Thompson plans to make jars of homemade salsa and pickles, using 6 tomatoes per jar of salsa and 10 cucumbers per jar of pickles. How many jars of salsa and jars of pickles can Mrs. Thompson make with her harvest?
answer:To solve the problem, we need to determine how many jars of salsa and pickles Mrs. Thompson can make with her harvest of tomatoes and cucumbers.Step 1: Calculate the total number of tomatoes.Mrs. Thompson has 24 tomato plants, and each plant produces 8 tomatoes.[text{Total tomatoes} = 24 times 8 = 192 text{ tomatoes}]Step 2: Calculate the total number of cucumbers.Mrs. Thompson has 18 cucumber plants, and each plant yields 5 cucumbers.[text{Total cucumbers} = 18 times 5 = 90 text{ cucumbers}]Step 3: Calculate the number of jars of salsa that can be made.Each jar of salsa requires 6 tomatoes.[text{Jars of salsa} = leftlfloor frac{192}{6} rightrfloor = leftlfloor 32 rightrfloor = 32 text{ jars of salsa}]Step 4: Calculate the number of jars of pickles that can be made.Each jar of pickles requires 10 cucumbers.[text{Jars of pickles} = leftlfloor frac{90}{10} rightrfloor = leftlfloor 9 rightrfloor = 9 text{ jars of pickles}]Final Answer:Mrs. Thompson can make 32 jars of salsa and 9 jars of pickles.# 32 jars of salsa and 9 jars of pickles
question:Jamie is a data analyst who loves using math to help companies make better decisions. One day, Jamie was analyzing sales data for a toy company. The company sells three types of toys: action figures, puzzles, and board games.In January, the company sold 120 action figures, 85 puzzles, and 95 board games. Jamie noticed that if they can increase the sales of each type of toy by 20%, they can reach their sales target for February.To help the company plan, Jamie needs to calculate the new sales target for each type of toy. How many action figures, puzzles, and board games should the company aim to sell in February?
answer:To solve this problem, we need to calculate the new sales target for each type of toy by increasing the January sales by 20%.Step 1: Calculate 20% of the January sales for each type of toy.- For action figures: - January sales = 120 - 20% of 120 = 0.20 × 120 = 24- For puzzles: - January sales = 85 - 20% of 85 = 0.20 × 85 = 17- For board games: - January sales = 95 - 20% of 95 = 0.20 × 95 = 19Step 2: Add the 20% increase to the January sales to find the February sales target.- For action figures: - New sales target = January sales + 20% increase = 120 + 24 = 144- For puzzles: - New sales target = January sales + 20% increase = 85 + 17 = 102- For board games: - New sales target = January sales + 20% increase = 95 + 19 = 114Final Answer:# 144 action figures, 102 puzzles, 114 board games
question:Clara is a singer-songwriter who loves to relax and find inspiration by listening to her vinyl records. She has 12 records in her collection, and each record has an average of 8 songs. Each time Clara listens to a record, she gets inspired to write 3 new songs. If Clara listens to all her vinyl records once, how many new songs will she be inspired to write in total?
answer:To solve this problem, we need to determine how many new songs Clara will be inspired to write after listening to all her vinyl records once.Step 1: Identify the total number of records in Clara's collection.- Clara has 12 records.Step 2: Determine how many new songs she is inspired to write after listening to one record.- Clara is inspired to write 3 new songs after listening to one record.Step 3: Calculate the total number of new songs Clara will be inspired to write after listening to all her records once.- Since Clara has 12 records and she writes 3 new songs per record, we multiply the number of records by the number of songs inspired per record: [ 12 text{ records} times 3 text{ songs per record} = 36 text{ new songs} ]Therefore, after listening to all her vinyl records once, Clara will be inspired to write a total of 36 new songs.# 36
question:Maria is a database administrator responsible for maintaining and optimizing data storage at her company. One of her tasks is to ensure that the company's databases are running efficiently. She has three databases: Database A, Database B, and Database C. Database A currently uses 120 GB of storage space, Database B uses 150 GB, and Database C uses 90 GB. Maria has been tasked with optimizing these databases to reduce their total storage usage by 20%. After optimizations, Database A's storage is reduced by 15%, Database B's storage is reduced by 25%, and Database C's storage is reduced by 30%.What is the total storage space used by all three databases after the optimizations?
answer:To solve the problem, we need to calculate the new storage space for each database after the optimizations and then find the total storage space used by all three databases.1. Initial Storage Space: - Database A: 120 GB - Database B: 150 GB - Database C: 90 GB2. Calculate the New Storage for Each Database: - Database A: - Reduction: 15% of 120 GB - Amount reduced = ( 120 times 0.15 = 18 ) GB - New storage = ( 120 - 18 = 102 ) GB - Database B: - Reduction: 25% of 150 GB - Amount reduced = ( 150 times 0.25 = 37.5 ) GB - New storage = ( 150 - 37.5 = 112.5 ) GB - Database C: - Reduction: 30% of 90 GB - Amount reduced = ( 90 times 0.30 = 27 ) GB - New storage = ( 90 - 27 = 63 ) GB3. Calculate the Total Storage After Optimization: - Total storage = New storage of Database A + New storage of Database B + New storage of Database C - Total storage = ( 102 + 112.5 + 63 = 277.5 ) GBThe total storage space used by all three databases after the optimizations is 277.5 GB.# 277.5 GB
question:A pest exterminator named Sam is treating a house for ants. Sam knows that without the right knowledge of entomology, he must rely on a systematic approach to ensure success. He estimates that there are 150 ants in the living room, 120 ants in the kitchen, and 80 ants in the bathroom. Sam's treatment can eliminate 70% of the ants in any room. After the treatment, how many ants are left in the house altogether?
answer:To solve this problem, we need to determine the number of ants remaining in each room after the treatment and then sum these amounts for the entire house.1. Determine the number of ants eliminated in each room: - Living Room: - Initial number of ants = 150 - Percentage of ants eliminated = 70% - Number of ants eliminated = 70% of 150 = 0.70 × 150 = 105 - Kitchen: - Initial number of ants = 120 - Percentage of ants eliminated = 70% - Number of ants eliminated = 70% of 120 = 0.70 × 120 = 84 - Bathroom: - Initial number of ants = 80 - Percentage of ants eliminated = 70% - Number of ants eliminated = 70% of 80 = 0.70 × 80 = 562. Calculate the number of ants remaining in each room: - Living Room: - Remaining ants = Initial ants - Ants eliminated = 150 - 105 = 45 - Kitchen: - Remaining ants = Initial ants - Ants eliminated = 120 - 84 = 36 - Bathroom: - Remaining ants = Initial ants - Ants eliminated = 80 - 56 = 243. Sum the remaining ants in all rooms to find the total number of ants left in the house: - Total remaining ants = Remaining ants in Living Room + Remaining ants in Kitchen + Remaining ants in Bathroom - Total remaining ants = 45 + 36 + 24 = 105Therefore, the total number of ants left in the house after the treatment is # 105