For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix.
61. Jay has lemon, orange, and pomegranate trees in his backyard. An orange weighs 8 oz, a lemon 5 oz. and a pomegranate 11 oz. Jay picked 142 pieces of fruit weighing a total of 70 1b, 10 oz. He picked 15.5 times more oranges than pomegranates. How many of each fruit did Jay pick?
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- For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 54. A food drive collected two different types of canned goods, green beans and kidney beans. The total number of collected cans was 350 and the total weight of all donated food was 348 1b, 12 oz. If the green bean cans weigh 2 oz less than the kidney bean cans, how many of each can was donated?arrow_forwardFor the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 59. Three roommates shared a package of 12 ice cream bars, but no one remembers who ate how many. If Tom ate twice as many ice cream bars as Joe, and Albert ate three less than Tom, how many ice cream bars did each roommate eat?arrow_forwardFor the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 55. Students were asked to bring their favorite fruit to class. 95% of the fruits consisted of banana, apple, and oranges. If oranges were twice as popular as bananas, and apples were 5% less popular than bananas, what are the percentages of each individual fruit?arrow_forward
- For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 60. A farmer constructed a chicken coop out of chicken wire, wood, and plywood. The chicken wire cost $2 per square foot, the wood $10 per square foot, and the plywood $5 per square foot. The farmer spent a total of $51, and the total amount of materials used was 14 ft2. He used 3 ft2 more chicken wire than plywood. How much of each material in did the farmer use?arrow_forwardFor the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 58. Anna, Ashley, and Andrea weigh a combined 370 lb. If Andrea weighs 20 1b more than Ashley, and Anna weighs 1.5 times as much as Ashley, how much does each girl weigh?arrow_forwardFor the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 53. In the previous exercise, if you were told there were 400 more tickets sold for floor 2 than floor l, how much was the price of each ticket?arrow_forward
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- For the following exercises, write the augmented matrix from the system of linear equations. 4x+2y3z=1412x+3y+z=1009x6y+2z=31arrow_forwardFor the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. 58. The three most popular ice cream flavors are chocolate, strawberry, and vanilla, comprising 83% of the flavors sold at an ice cream shop. If vanilla sells 1% more than twice strawberry, and chocolate sells 11% more than vanilla, how much of the total ice cream consumption are the vanilla, chocolate, and strawberry flavors?arrow_forwardFor the following exercises, write the system of linear equations from the augmented matrix. Indicate whether there will be a unique solution. [10501 2000|943]arrow_forward