Graphing & Analyzing Real-World Systems of Equations

A car travels 60 miles in 1 hour and another car travels 90 miles in 1.5 hours. Write a system of equations to represent the distance each car travels over time. Graph the equations and analyze the intersection point.

• The system of equations is d1 = 60t and d2 = 90t, suggesting the second car travels faster but not over time.

• The system of equations is d1 = 60t and d2 = 60t, indicating both cars travel at the same speed.

• The system of equations is d1 = 30t and d2 = 45t, showing both cars travel slower than their actual speeds.

• The system of equations is d1 = 60t and d2 = 90t, indicating different speeds.

A mixture of two solutions contains 30% salt and 70% water. If you mix 5 liters of this solution with another solution that is 10% salt, write a system of equations to find the total amount of salt in the mixture. Graph the equations and analyze the solution set.

• Total amount of salt = 1.5 + 0.10z liters, where z is the volume of the second solution.

• Total amount of salt = 2 + 0.05z liters

• Total amount of salt = 1 + 0.15z liters

• Total amount of salt = 1.2 + 0.20z liters

Two friends are selling lemonade and cookies. They sell lemonade for $2 per cup and cookies for $1 each. If they make a total of $50 selling 30 items, write a system of equations to represent their sales. Graph the equations and find the number of cups of lemonade sold.

• 25

• 10

• 15

• 20

A train travels at a speed of 50 miles per hour and a bus travels at 30 miles per hour. If they start from the same point and travel for 2 hours, write a system of equations to represent the distance each vehicle travels. Graph the equations and analyze the solution set.

• d_t = 60t, d_b = 20t

• d_t = 50t, d_b = 50t

• The system of equations is: d_t = 50t, d_b = 30t.

• d_t = 40t, d_b = 30t

A store sells pencils for $0.50 each and erasers for $1.00 each. If a student buys a total of 20 items and spends $12, write a system of equations to represent the situation. Graph the equations and find the number of pencils purchased.

• 18

• 14

• 12

• 16

A tank contains a mixture of 40 liters of water and 10 liters of juice. If you add 20 liters of water to the tank, write a system of equations to find the new concentration of juice in the mixture. Graph the equations and analyze the solution set.

• The new concentration of juice is 25%.

• The new concentration of juice in the mixture is approximately 0.142857 or 14.29%.

• The new concentration of juice is 10%.

• The new concentration of juice is 5%.

Two types of fruit are mixed together: apples and oranges. If the total weight of the mixture is 15 kg and the weight of the apples is twice that of the oranges, write a system of equations to represent the situation. Graph the equations and analyze the solution set.

• Weight of apples: 10 kg, Weight of oranges: 5 kg

• Weight of apples: 12 kg, Weight of oranges: 3 kg

• Weight of apples: 7 kg, Weight of oranges: 8 kg

• Weight of apples: 5 kg, Weight of oranges: 10 kg

A cyclist travels 12 miles in 1 hour and a runner travels 6 miles in 0.5 hours. Write a system of equations to represent their speeds. Graph the equations and analyze the intersection point to find when they will meet.

• They will meet at every point along their paths.

• They will never meet during their travels.

• The cyclist will always be ahead of the runner.

• They will meet at a specific point after 2 hours.