The manager of a movie theater noted that 411 people attended a movie but neglected to note the number of adults and children. Admission was $7.00 for adults and $3.75 for children. The receipts were $2678.75. How many adults and children attended the movie? X = Movie Attendees Amount Value Total Adults a $7.00 7 a Children c $3.75 3.75c Mix a + c = 411 $2678.75 7a + 3.75c = 2678.75 1. Variable statement: a = adults c = children 2. Equations: a + c = 411 7a + 3.75c = 2678.75 -c = - c a = 411 c 7(411 c) + 3.75c = 2678.75 – – 2877 7c + 3.75c = 2678.75 – 2877 3.25 c = 2678.75 – - 2877 = -2877__ - 3.25 c = -198.25 -3.25 -3.25 c = 61 a = 411 61 – a = 350 Solution: a = 350 adults c = 61 children V. Distance Problems: D = R x T A. The distance between Houston, Texas and Austin, Texas is 180 miles. A car leaves Houston traveling toward Austin at an average rate of 68 miles per hour. At the same time, a van leaves Austin traveling toward Houston at an average rate of 52 miles per hour. Assuming they are traveling on the same route, how long will it take until they meet? / d r t Car Van
The manager of a movie theater noted that 411 people attended a movie but neglected to note the number of adults and children. Admission was $7.00 for adults and $3.75 for children. The receipts were $2678.75. How many adults and children attended the movie? X = Movie Attendees Amount Value Total Adults a $7.00 7 a Children c $3.75 3.75c Mix a + c = 411 $2678.75 7a + 3.75c = 2678.75 1. Variable statement: a = adults c = children 2. Equations: a + c = 411 7a + 3.75c = 2678.75 -c = - c a = 411 – c 7(411 – c) + 3.75c = 2678.75 2877 – 7c + 3.75c = 2678.75 2877 – 3.25 c = 2678.75 - 2877 = -2877__ - 3.25 c = -198.25 -3.25 -3.25 c = 61 a = 411 – 61 a = 350 Solution: a = 350 adults c = 61 children V. Distance Problems: D = R x T A. The distance between Houston, Texas and Austin, Texas is 180 miles. A car leaves Houston traveling toward Austin at an average rate of 68 miles per hour. At the same time, a van leaves Austin traveling toward Houston at an average rate of 52 miles per hour. Assuming they are traveling on the same route, how long will it take until they meet? d r t Car Van /
Chapter_10_Reading.docx