Unit 3 Challenge 3: College Algebra In Context - All questions

Unit 3 Challenge 3: College Algebra In Context 1. Solving Mixture Problems using a System of Equations Riley wants to make 100 mL of a 25% saline solution but only has access to 12% and 38% saline mixtures. Which o ...

Unit 3 Challenge 3: College Algebra In Context 1. Solving Mixture Problems using a System of Equations Riley wants to make 100 mL of a 25% saline solution but only has access to 12% and 38% saline mixtures. Which of the following system of equations correctly describes this situation if represents the amount of the 12% solution used, and represents the amount of the 38% solution used? • b.) • b.)Correct.One equation in the system will represent the relationship between the quantity and the concentration: 0.12x+0.38y = 0.25(100). Here each quantity, x and y, are multiplied by their respective percent concentrations, 12% and 38%. Also, when we add these two together, they should be 100 mL of 25% solution, which can be expressed as 0.25(100). The other equation needs to relate the quantities. Together, the amount of 12% and the amount of 38% needs to total 100 mL. So x + y = 100. Makayla wants to make 200 mL of a 18% saline solution but only has access to 8% and 24% saline mixtures. 2 of 16 Which of the following system of equations correctly describes this situation if represents the amount of the 8% solution used, and represents the amount of the 24% solution used? • a.) a.)Correct. One equation in the system will represent the relationship between the quantity and the concentration: 0.08+0.24 = 0.018(200). Here each quantity, x and y, is multiplied by their respective percent concentrations, 8% and 24%. Also, when we add these two together, they should be 200 mL of 18% solution, which can be expressed as 0.18(200). The other equation needs to relate the quantities. Together, the amount of 8% and the amount of 24% needs to total 200 mL. So x + y = 200. Connor has $100,000 and wants to get an 8% return total at the end of the year. He can invest in two different stocks. One of the stocks will yield a 6% return per year and the second will yield a 8.5% return per year. Which of the following system of equations correctly describes this situation if represents the amount invested in the 6% stock, and represents the amount invested in the 8.5% stock? c.) 3 of 16 .)Correct. One equation in the system will represent the relationship between the quantity and the percent: 0.06x+0.085y = 0.08(100000). Here each quantity, x and y, is multiplied by their respective percents, 6% and 8.5%. Also, when we add these two together, they should equal 8% of $100,000, which can be expressed as 0.08(100000). The other equation needs to relate the quantities. Together, the amount invested in 6% return and the amount invested in 8.5% return needs to equal the total amount invested, which is $100,000. So x + y = 100000. 2. Distance, Rate, and Time in a System of Equations When traveling with the current, it takes Kamal 1 hour to travel 12 miles on a boat. It takes the boat 1.5 hours to travel the same 12 miles when traveling against the current. Assuming the boat travels at a constant speed during both trips, what is the speed of the boat and the speed of the current? Boat's speed: 10 miles per hour Current's speed: 2 miles per hour b.)Correct. The current will work in the favor of the boat when it is traveling with the current, but make the boat go slower when it is traveling against the current. Let the speed of the boat be and the speed of the current be . When the rates are working together, the boat travels 12 miles in 1 hour, which can be expressed as: 4 of 16 When the rates are working against each other, the boat travels 12 miles in 1.5 hours, which can be expressed as: Next create equivalent equations by dividing each equation by its respective time: and Add the equations together to cancel The speed of the boat is 10 miles per hour. Substitute this value into any equation to find a value of