Modeling with Matrices Answers

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 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?

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?

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?

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 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?

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?

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?

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?