University:
High School
Course:
High School Algebra
Academic year:

2019
Views:

427

Pages:

2
Author:

tremblavi7u

Systems Word Problems Using system of equations to solve. There are three types of word problems that a system of equations can help us solve. Coin Problems Quarters: 25¢ Dimes: 10¢ Nickels: 5¢ Pennies: 1¢ Count Total = A + B + ... Value Total = (ValueA)(#A) + (ValueB)(#B) General Problems Tickets Gerbils Circles Count Total = A + B Value Total = (ValueA)(#A) + (ValueB)(#B) Motion Problems Distance = (rate)(time) Draw a picture Opposite direction: + Same direction: - (rate)(time)A ± (rate)(time)B = Distance Set-Up Kevin has 3 more than twice as many dimes as quarters. If the value of his money is $3.45, how many of each coin does he have? .25q + .10d = 3.45 d = 3 + 2q The attendance at a school concert was 578. Admission cost $2 for adults and $1.50 for children. The receipts were $985. How many adults and how many children attended the concert? Count: 578 = a + c Value: 985 = 2a + 1.5c Two cars leave town, traveling in opposite directions. The first car travels at 50 mph, and the second travels at 60 mph. How long will it take them to be 100 miles apart? 50t + 60t = 100 One car travels 56 mph and another travels 31 mph. If they start from the same place at the same time, traveling in the same direction, after how many hours will the faster car be 42 miles ahead of the slower one? 42 = 56h - 31h Set-Up and now solve Two trains travel for eleven hours, starting from the same place and traveling in opposite directions. One train travels at a rate that is 15 mile per hour faster than the other. Find the rate of each train if they are 291 miles apart after three hours. 3(r) + 3(r + 15) = 291 On a table there are 20 coins, some quarters and some dimes. Their value is $3.05. How many of each are there? 20 = q + d 305 = 25q + 10d A collection of 8 coins is worth $3.95. There are eight more dimes than nickels. How many of each coin? d = 8 + n 395 = 5n + 10d Dance tickets cost $5 with ASB sticker and $8 without ASB. 300 tickets were sold to a dance, with $1740 collected. How many of each type of ticket was sold? 5a + 8w = 1740 a + w = 300 Two airplanes start at the same place and travel in opposite directions, one at 520 miles per hour and the other at 448 miles per hour. How many hours will it take for them to be 1936 miles apart? 520h + 448h = 1936 One car travels 50 miles per hour and another travels 55 miles per hour. If they start from the same place at the same time and travel in the same direction, after how many hours will the faster car be 35 miles ahead of the slower car? 35 = 55h - 50h Two freight trains started at the same time from towns 564 miles apart and met in 6 hours. The average rate of one train was 14 miles per hour faster than that of the other train. Find the rate of each train. 564 = (r)(6) + (r + 14)(6) Two cars start at the same place and travel in opposite directions, one at 63 mph and the other at 49mph. After how many hours are they 840 miles apart? 840 = 63h + 49h One bus travels 60 mph and another travels 35 mph. If they start from the same place at the same time, how long will it take for the faster bus to be 20 miles ahead of the slower one? 20 = 60h - 35h