Modeling with Matrices Answers

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 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 detergent is created by mixing washing soda, borax, and water. The table below shows the composition of three different detergents. Composition of Detergents ABCWashing Soda0.050.150.20Water0.800.800.70Borax0.150.050.10Travis needs to use a combination of the detergents to create 100 ounces of a detergent that is 15% washing soda, 75% water, and 10% borax. Which is true?

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?

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?

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?

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?

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?

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?

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?