For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule.
65. At a women's prison down the road, the total number of inmates aged 20 - 49 totaled 5,525. This year, the 20 - 29 age group increased by 10%, the 30 - 39 age group decreased by 20%, and the 40 - 49 age group doubled. There are now 6,040 prisoners. Originally, there were 500 more in the 30-39 age group than the 20-29 age group. Determine the prison population for each age group last year.
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
College Algebra
Additional Math Textbook Solutions
College Algebra (7th Edition)
Intermediate Algebra (7th Edition)
College Algebra (10th Edition)
Linear Algebra with Applications (2-Download)
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
Introductory and Intermediate Algebra for College Students (5th Edition)
- What is a system of linear equations in the variables x, y, and z?arrow_forwardFor the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 61. At the same market, the three most popular fruits make up 37% of the total fruit sold. Strawberries sell twice as much as oranges, and kiwis sell one more percentage point than oranges. For each fruit, find the percentage of total fruit sold.arrow_forwardFor the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 55. A movie theater needs to know how many adult tickets and children tickets were sold out of the 1,200 total tickets. If children's tickets are $5.95, adult tickets are $11.15, and the total amount of revenue was $12,756, how many children's tickets and adult tickets were sold?arrow_forward
- Use the system of three equations in three variables to solve each problem. Work schedules A college student earns 198.50 per week working three part-time jobs. Half of his 30-hour work week is spent cooking hamburgers at a fast-food chain, earning 5.70 per hour. In addition, the student earns 6.30 per hour doing janitorial work. How many hours per week does the student work at each jobarrow_forwardFor the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 62. Three bands performed at a concert venue. The first band charged $15 per ticket, the second band charged $45 per ticket, and the final band charged $22 per ticket. There were 510 tickets sold, for a total of $12,700. If the first band had 40 more audience members than the second band, how many tickets were sold for each band?arrow_forwardTranslate to a system of equations and then solve: Charlie left his mother’s house traveling at an average speed of 36 miles per hour. His sister Sally left 15 minutes (1/4 hour) later traveling the same route at an average speed of 42 miles per hour. How long before Sally catches up to Charlie?arrow_forward
- For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 57. You decide to paint your kitchen green. You create the color of paint by mixing yellow and blue paints. You cannot remember how many gallons of each color went into your mix, but you know there were 10 gal total. Additionally, you kept your receipt, and know the total amount spent was $29.50. If each gallon of yellow costs $2.59, and each gallon of blue costs $3.19, how many gallons of each color go into your green mix?arrow_forwardFor the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 56. A concert venue sells single tickets for $40 each and couple's tickets for $65. If the total revenue was $18,090 and the 321 tickets were sold, how many single tickets and how many couple's tickets were sold?arrow_forwardFor the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 58. You sold two types of scarves at a farmers' market and would like to know which one was more popular. The total number of scarves sold was 56, the yellow scarf cost $10, and the purple scarf cost $11. If you had total revenue of $583, how many yellow scarves and how many purple scarves were sold?arrow_forward
- For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. 60. At a market, the three most popular vegetables make up 53% of vegetable sales. Corn has 4% higher sales than broccoli, which has 5% more sales than onions. What percentage does each vegetable have in the market share?arrow_forwardTranslate to a system of equations and then solve: Alexis wants to build a rectangular dog run in her yard adjacent to her neighbor’s fence. She will use 136 feet of fencing to completely enclose the rectangular dog run. The length of the dog run along the neighbor’s fence will be 16 feet less than twice the width. Find the length and width of the dog run.arrow_forwardTranslate to a system of equations and then solve: Mitchell left Detroit on the interstate driving south towards Orlando at a speed of 60 miles per hour. Clark left Detroit 1 hour later traveling at a speed of 75 miles per hour, following the same route as Mitchell. How long will it take Clark to catch Mitchell?arrow_forward
- Elementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice University
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill