Modeling with Matrices Answers

Jeremy’s fruit stand sells peaches and watermelons. In the first hour the fruit stand is open, 12 bushels of peaches and 5 watermelons are sold for a total of $150. In the second hour, 15 bushels of peaches and 8 watermelons are sold for a total of $198. A bushel of peaches costs p dollars, and a watermelon costs w dollars. Which matrix equation represents the situation?

A trail mix is made up of peanuts that cost p dollars per pound and dried fruit that costs d dollars per pound. A blend of pound of peanuts and pound of dried fruit costs $6.50. A blend of pound of peanuts and pound of dried fruit costs $4.50. Which matrix equation can be used to solve for the cost of 1 pound of peanuts and the cost of 1 pound of dried fruit?

A chemist has a container of 12% peroxide solution and a container of 20% peroxide solution. She needs to mix the two solutions to create 100 mL of a 14% solution. If x represents the amount of 12% peroxide solution and y represents the amount of 20% peroxide solution she needs, which matrix equation can determine the amount of each solution she needs to make the 14% solution?

Elise, Maggie, and Francesca work for an insurance company making follow-up calls to clients. Each person works at a different rate. The table below shows the number of hours each person works over three days and the total number of calls that are made. Hours Worked and Total Calls Made EliseMaggieFrancescaTotal CallsMonday778247Tuesday659218Wednesday931156Elise makes the same number of calls every hour, Maggie makes the same number of calls every hour, and Francesca makes the same number of calls every hour. If Elise earns $1.50 per phone call, how much money does Elise make over the 3 days?

An office building has three air conditioning units, one for each office. Each unit runs only when employees are working. The tables below show the number of hours employees worked at each office over a three-month period and the total air conditioning electric costs for the entire office for each month. Number of Hours Worked Unit AUnit BUnit CJune184207276July174198264August168189242Total Air Conditioning Electric CostsJune$142.60July$135.96August$128.30How much does it cost to run Unit A per hour?

Indira has 18 coins valued at $4.20. She has only quarters and dimes. Which augmented matrix can be used to determine the number of quarters and dimes in the collection?

A company sells herb blends for cooking. The tables below show the number of teaspoons of each herb in each blend and the cost for each blend. Number of Teaspoons of Herb per Blend BasilOreganoParsleyBlend 1123Blend 2112Blend 3221 CostBlend 1$1.06Blend 2$0.72Blend 3$0.99What is the cost of basil per teaspoon?

The table below shows the composition of three mixtures of nuts. Composition of Nut Mixtures Mixture AMixture BMixture CPecans0.600.500.75Almonds0.300.450.15Walnuts0.100.050.10Mr. Murray wants to create 100 ounces of a mixture that is 62% pecans, 30% almonds, and 8% walnuts. How will the amount of Mixture A compare to the amounts of Mixtures B and C that Mr. Murray uses?

A test is worth 100 points. The test is made up of 40 items. Each item is worth either 2 points or 3 points. Which matrix equation and solution represent the situation?

For a client, a landscaper purchases 3 oak trees and 4 maple trees for $380. For his own home, the landscaper purchases 2 oak trees and 5 maple trees for $370. Which augmented matrix represents the situation?