Modeling with Systems of Linear Equations — Quiz Answers

A motorboat travels 9 miles downstream (with the current) in 30 minutes. The return trip upstream (against the current) takes 90 minutes. Which system of equations can be used to find x , the speed of the boat in miles per hour, and y , the speed of the current in miles per hour? Recall the formula d is equal to rt .

Adele is 5 years older than Timothy. In three years, Timothy will be 2 thirds of Adele’s age. What is Adele’s current age?

Each month, Kaisorn deposits 50 point 00 dollars onto her public transportation card. It costs her 2 point 50 dollars per trip to ride the subway. Thom deposits 40 point 00 dollars on his public transportation card. It costs him 2 point 00 dollars per trip to ride the subway. If x represents the number of trips and y represents the amount remaining in each account, which system of equations represents their transportation costs?

A pilot flew a 400 -mile flight in 2 point 5 hours flying into the wind. Flying the same rate and with the same wind speed, the return trip took only 2 hours, with a tailwind. What was the speed of the wind?

A business owner pays 1 dollars comma 200 per month in rent and a total of 120 dollars per hour in employee salaries for each hour the store is open. On average, the store brings in 200 dollars in net sales per hour. Which equations can be solved to determine the break-even point if C times x represents the cost function, R times x represents the revenue function, and x the number of hours per month the store is open?

Zorah, a musician, pays 120 dollars to have her instrument tuned and 10 dollars per hour for a booth at a fair. She estimates that she earns 25 dollars per hour in tips. The equation can be used to represent the break-even point. 120 plus 10 x is equal to 25 x How many hours, x , will Zorah have to play in order to break even?

Bethany has 3 point 10 dollars in nickels and dimes. She has a total of 44 coins. What is the value of the nickels Bethany has?

A salesperson earns a commission based on the number and type of vehicle sold. A person selling 6 cars and 3 trucks earns 4 dollars comma 800 A person selling 8 cars and 1 truck earns 4 dollars comma 600 How much does a salesperson earn for selling 2 cars and 3 trucks?

An aircraft travels with the wind for 120 miles in 0 point 75 of an hour. The return trip is flown against the wind and takes exactly 1 hour. Which system of linear equations represents x , the speed of the plane in miles per hour, and y , the speed of the wind in miles per hour? Recall the formula d is equal to r t

A store sells both cold and hot beverages. Cold beverages, c , cost 1 point 50 dollars , while hot beverages, h , cost 2 point 00 dollars On Saturday, drink receipts totaled 360 dollars , and 4 times as many cold beverages were sold as hot beverages. Which system of linear equations represents the beverage sales on Saturday?