Formulate a system of equations for the situation below and solve.A theater has a seating capacity of 900 and charges $4 for children, $6 for students, and $8 for adults. At a certain screening with full attendance, there were half as many adults aschildren and students combined. The receipts totaled $5600. How many children attended the show?childrenTEACHERPRACTICE ANOTHER

Let number of the children=x Let number of the students=y Let number of the adults=z Since the full…

Answered: Formulate a system of equations for the…

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter4: Systems Of Linear Equations

Section4.2: Solve Applications With Systems Of Equations

Problem 4.43TI: Translate to a system of equations and then solve: A Mississippi river boat cruise sailed 120 miles...

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Translate to a system of equations and solve: Greta wants to make 5 pounds of a nut mix using peanuts and cashews. Her budget requires the mixture to cost her $6 per pound. Peanuts are $4 per pound and cashews are $9 per pound. How many pounds of peanuts and how many pounds of cashews should she use?
Translate 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.
Translate to a system of equations and then solve: Jake’s dad is 6 more than 3 times Jake’s age. The sum of their ages is 42. Find their ages.
Translate to a system of equations and solve: Anatole needs to make 250 milliliters of a 25% solution of hydrochloric acid for a lab experiment. The lab only has a 10% solution and a 40% solution in the storeroom. How much of the 10% and how much of the 40% solutions should he mix to make the 25% solution?
Translate to a system of equations and then solve: A commercial jet can fly 1,728 miles in 4 hours with a tailwind but only 1,536 miles in 4 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.
Translate to a system of equations and then solve: Erin spent 30 minutes on the rowing machine and 20 minutes lifting weights at the gym and burned 430 calories. During her next visit to the gym she spent 50 minutes on the rowing machine and 10 minutes lifting weights and burned 600 calories. How many calories did she burn for each minutes on the rowing machine? How many calories did she burn for each minute of weight lifting?
Translate to a system of equations and then solve: Mark went to the gym and did 40 minutes of Bikram hot yoga and 10 minutes of jumping jacks. He burned 510 calories. The next time he went to the gym, he did 30 minutes of Bikram hot yoga and 20 minutes of jumping jacks burning 470 calories. How many calories were burned for each minute of yoga? How many calories were burned for each minute of jumping jacks?
Translate to a system of equations and then solve: Ali is 12 years older than his youngest sister, Jameela. The sum of their ages is 40. Find their ages.
For each system of linear equations, decide whether it would be more convenient to solve it by substitution or elimination. Explain your answer. (a) {4x5y=323x+2y=1 (b) {x=2y13x5y=7
Translate to a system of equations and then solve: Mario wants to put a rectangular fence around the pool in his backyard. Since one side is adjacent to the house, he will only need to fence three sides. There are two long sides and the one shorter side is parallel to the house. He needs 155 feet of fencing to enclose the pool. The length of the long side is 10 feet less than twice the width. Find the length and width of the pool area to be enclosed.
Translate to a system of equations and then solve: Mario wants to put a fence around the pool in his backyard. Since one side is adjacent to the house, he will only need to fence three sides. There are two long sides and the one shorter side is parallel to the house. He needs 155 feet of fencing to enclose the pool. The length of the long side is 10 feet less than twice the width. Find the length and width of the pool area to be enclosed.
Solve the system of equations by elimination and explain all your steps in words: {5x+4y=102x=3y+27 .

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