System of Equations-Word Problems

There are 15 plates in the kitchen cabinet. The diameter of each plate if 7 inches or 12 inches. The diameter of all 15 plates combines is 140 inches. Which system of equations can be used to find the number of 7-inch plates, x, and the number of 12-inch plates, y, that are in the cabinet? x + y = 1512x + 7y = 140 x + y = 14012x + 7y = 15 7x + 12y = 1407x + 12y = 15 x + y = 157x + 12y = 140 A drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote. They wrote a total of 46 songs. Which system of equations models this situation, if the drummer wrote d songs and the guitarist, wrote g songs? g = 2d - 8g + d = 46 g = 8 - 2dg = 46 - d d = 2g - 8d = 46 - g d = 8 - 2gd + g = 46 Read the word problem along with its system of equations to fill in the necessary missing pieces of information. A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85. The system of equations is provided and can be used to determine the number of quarters, q, and the number of dimes, d, in the bag..25 q + .10 d = 2.85q + d = 18 Tracy and Juan went to the concession stand at the ballpark to buy snacks for their friends. Tracy spent $4 for 3 bags of popcorn and 2 candy bars. Juan spent $4 for 2 bags of popcorn and 4 candy bars. Write a system of linear equations that could be used to determine how much was spend on bags of popcorn and candy bars. Tickets to the spring concert cost either $8.50 or $12.75, based on the purchaser’s age. A total of 450 tickets were sold for all of the performances. A total of $4,662.25 was collected in ticket sales. Write a system of linear equations that can be used to determine the number of $8.50 tickets sold and the number of $12.75 tickets sold. A college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses. How many courses worth 3 credits did the student complete? 5 13 20 39 Read the word problem along with its system of equations to fill in the necessary missing pieces of information. A busy coffee shop purchased a total of 77 donuts and muffins. The cost of a muffin is 2.5 times the cost of a donut. Write a system of equations that can be used to determine the number of donuts, x, and the number of muffins, y, purchased by the coffee shop.x + y = 772.5 x = y A bag contains 77 coins consisting of quarters and nickels. The total value of the coins is $12.50. Write a system of equations that can be used to determine the number of quarters, x, and the number of nickels, y,in the bag. x + y = 770.25x + 0.5y = 12.5 0.25x +0.5 y = 77x + y = 12.5 x + y = 770.25x + 0.05y = 12.5 0.25x + 0.05y =77x + y = 12.5 Rob has 4 bills in his pocket that total $23. He only has twenty-dollar bills and one-dollar bills. a + b = 4; 20a + b = 23 Sally has 4 more baseball cards in her collection than her brother. Together they have a total of 20 baseball cards. a - b = 4; a + b = 20 Charlottte went to the candy store. The bag of milk chocolate has 4 more bars of candy than the bag of dark chocolate. The total number of bars in 2 bags of milk chocolate and 3 bags of dark chocolate is 23. 2a + 3b = 23; a - b = 4 Walt purchases meals and tickets for a theme park. Three meals cost $23 more than a ticket. Two meals cost $2 more than a ticket. 3a - b = 23; 2a - b = 2 adult tickets purchased children's tickets purchased a + c = 2350 6a + 2.5c = 8640 Describe what each part of the system of equations represents in the context of the scenario. Mr. Byrnes gives his Algebra 1 class a test with 2 different types of questions: multiple choice and open-ended. Each type of question is worth a different point value, with multiple choice worth less than opened ended. the number of opened ended questions the total number of questions the number of multiple choice questions point value of each multiple choice total points possible on the multiple choice point value of each open ended total points possible on the open ended total points possible on the test. Read the word problem along with its system of equations to fill in the necessary missing pieces of information. A rectangle has a perimeter of 38 feet. Twice its length, h, is equal to four feet less than 5 times its width, w. What is the width of the rectangle?38 = 2h + 2w2h = 5 w - 4 Provide the missing information for the paragraph so that it represents the paired system oflinear equations. Then, answer the question. 416 478 14 beads for bracelets & 76 beads for necklaces. 5 necklaces 8 beaded bracelets