Modeling with Matrices Answers

The compositions of three powdered drink mixes are shown in the table below. Drink Mix Composition Mix AMix BMix CCitric Acid0.100.150.20Flavoring0.100.050.10Sugar0.800.800.70Xavier needs to create 100 grams of a drink mix containing 18% citric acid, 8% flavoring, and 74% sugar. How much of Mix C should he use?

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?

Jacy has a collection of 140 coins worth $19.00. She has only nickels, dimes, and quarters. The difference in the number of dimes and the number of quarters is 10. Using matrices, how many nickels are in Jacy’s collection?

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?

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?

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?

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 carnival charges each person an admission fee and a fee per ride. A family pays 6 admission fees, and they pay for a total of 20 rides. A couple pays 2 admission fees, and they pay for a total of 18 rides. The family pays a total of $64. The couple pays a total of $44. Which augmented matrix can be used to determine the cost per admission and the cost per ride?

Janelle is five years younger than Louisa. In three years, Janelle will be half Louisa’s age. If j represents Janelle’s age now and l represents Louisa’s age now, which matrices represent the situation?

Melissa made a total of 14 baskets during her last basketball game. She made a number of 2-point baskets and a number of 3-point baskets for a total of 33 points. Using matrices to solve, how many 3-point baskets did Melissa make in her last basketball game?