For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution.
61. A bag of mixed nuts contains cashews, pistachios, and almonds. Originally there were 900 nuts in the bag. 30% of the almonds, 20% of the cashews, and 10% of the pistachios were eaten, and now there are 770 nuts left in the bag. Originally, there were 100 more cashews than almonds. Figure out how many of each type of nut was in the bag to begin with.
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- For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. 60. A bag of mixed nuts contains cashews, pistachios, and almonds. There are 1,000 total nuts in the bag, and there are 100 less almonds than pistachios. The cashews weigh 3 g, pistachios weigh 4 g, and almonds weigh 5 g. If the bag weighs 3.7 kg, find out how many of each type of nut is in the bag.arrow_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_forwardWhat is a system of linear equations in the variables x, y, and z?arrow_forward
- For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. 53. At a competing cupcake store, $4,520 worth of cupcakes are sold daily. The chocolate cupcakes cost $2.25 and the red velvet cupcakes cost $1.75. If the total number of cupcakes sold per day is 2,200, how many of each flavor are sold each day?arrow_forwardWrite the system of equations that that corresponds to the augmented matrix. 200. [2113|42]arrow_forwardWhen Gloria spent 15 minutes on the elliptical trainer and then did circuit training for 30 minutes, her fitness app says she burned 435 calories. When she spent 30 minutes on the elliptical trainer and 40 minutes circuit training she burned 690 calories. Solve the system {15e+30c=43530e+40c=690 for e, the number of calories she burns for each minute on the elliptical trainer, and c, the number of calories she burns for each minute of circuit training.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. 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_forwardFor the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. 56. Bikes’R’Us manufactures bikes, which sell for $250. It costs the manufacturer $180 per bike, plus a startup fee of $3,500. After how many bikes sold will the manufacturer break even?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. 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. 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?arrow_forwardFor 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_forward
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