Modeling with Matrices Answers

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?

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?

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?

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 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?

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?

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?

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?

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?

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?

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 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?

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?

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 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?