B. State whether each problem is an example of a direct or an inverse proportion. Then, solve it. 1. A machine produces 275 chairs in 7.5 h. How long does it take to produce 730 chairs? 2. Eight bakers take 8 h to produce the daily bread requirement of a bakery How many bakers are required to produce the same quantity of bread in 6h? 3. Three sales agents sold a total of Php 534 000.00 worth of goods in a month How much could 9 sales agents sell in a month? 4. The average number of careless errors in a math assignment of 25 problems is 5. How many careless errors would you expect in a math assignment of 100 problems? 5. Fifteen persons can interview 1 200 homeowners for a survey in 5 days. the interview must be completed in 4 days with the same number of home owners, how many persons will be needed?
Answer (1)
Answer:Here are the solutions and explanations for each problem: 1. A machine produces 275 chairs in 7.5 h. How long does it take to produce 730 chairs?Type of Proportion: Direct Proportion (As the number of chairs increases, the time taken also increases proportionally)Solution: - Find the production rate: 275 chairs / 7.5 hours = 36.67 chairs per hour - Calculate the time: 730 chairs / 36.67 chairs per hour = 20 hoursAnswer: It takes 20 hours to produce 730 chairs. 2. Eight bakers take 8 h to produce the daily bread requirement of a bakery. How many bakers are required to produce the same quantity of bread in 6h?Type of Proportion: Inverse Proportion (As the time taken decreases, the number of bakers needed increases)Solution: - Calculate the total work: 8 bakers * 8 hours = 64 baker-hours - Find the number of bakers needed: 64 baker-hours / 6 hours = 10.67 bakers - Round up to the nearest whole number: 11 bakersAnswer: 11 bakers are required to produce the same quantity of bread in 6 hours. 3. Three sales agents sold a total of Php 534 000.00 worth of goods in a month. How much could 9 sales agents sell in a month?Type of Proportion: Direct Proportion (As the number of sales agents increases, the total sales also increase proportionally)Solution: - Find the sales per agent: Php 534,000 / 3 agents = Php 178,000 per agent - Calculate the total sales for 9 agents: Php 178,000 per agent * 9 agents = Php 1,602,000Answer: 9 sales agents could sell Php 1,602,000 worth of goods in a month. 4. The average number of careless errors in a math assignment of 25 problems is 5. How many careless errors would you expect in a math assignment of 100 problems?Type of Proportion: Direct Proportion (As the number of problems increases, the number of careless errors also increases proportionally)Solution: - Find the error rate: 5 errors / 25 problems = 0.2 errors per problem - Calculate the expected errors: 0.2 errors per problem * 100 problems = 20 errorsAnswer: You would expect 20 careless errors in a math assignment of 100 problems. 5. Fifteen persons can interview 1 200 homeowners for a survey in 5 days. The interview must be completed in 4 days with the same number of homeowners, how many persons will be needed? Type of Proportion: Inverse Proportion (As the time taken decreases, the number of persons needed increases)Solution: - Calculate the total work: 15 persons * 5 days = 75 person-days - Find the number of persons needed: 75 person-days / 4 days = 18.75 persons - Round up to the nearest whole number: 19 personsAnswer: 19 persons will be needed to complete the interviews in 4 days.
