Solving Real-World Systems of Equations: Grade 8 Challenge

A car travels 60 miles in 1 hour and 90 miles in 1.5 hours. How can you express the distance traveled as a system of equations?

• x = 90, t = 1 for the first scenario; x = 60, t = 2 for the second scenario.

• x = 60, t = 0.5 for the first scenario; x = 90, t = 1 for the second scenario.

• x = 30, t = 1 for the first scenario; x = 90, t = 1 for the second scenario.

• x = 60, t = 1 for the first scenario; x = 60, t = 1.5 for the second scenario.

Two types of juice are mixed: one is 30% orange juice and the other is 70% orange juice. If you mix 3 liters of the first with x liters of the second to get a 50% orange juice mixture, what is x?

• 3

• 1

• 10

• 5

A train leaves a station traveling at 80 miles per hour. Another train leaves the same station 30 minutes later traveling at 100 miles per hour. How far from the station will they meet?

• 15 miles

• 30 miles

• 40 miles

• 22.22 miles

A store sells two types of shirts: one for $20 and another for $30. If a customer buys a total of 5 shirts for $120, how many of each type did they buy?

• 4 shirts for $20 and 1 shirt for $30

• 3 shirts for $20 and 2 shirts for $30

• 1 shirt for $20 and 4 shirts for $30

• 2 shirts for $20 and 3 shirts for $30

A recipe requires a mixture of two types of flour: one is $2 per pound and the other is $3 per pound. If you need 10 pounds of flour for a total cost of $24, how many pounds of each type do you need?

• 6 pounds of $2 flour and 4 pounds of $3 flour

• 7 pounds of $2 flour and 3 pounds of $3 flour

• 8 pounds of $2 flour and 2 pounds of $3 flour

• 5 pounds of $2 flour and 5 pounds of $3 flour

A cyclist travels 15 miles at a speed of 10 miles per hour and then 25 miles at a speed of 15 miles per hour. How long did the entire trip take?

• 3 hours

• 4 hours

• 3.1667 hours

• 2.5 hours

Two friends are saving money to buy a video game. One saves $5 per week and the other saves $7 per week. If they want to save a total of $50 together, how many weeks will it take?

• 5 weeks

• 8 weeks

• 6 weeks

• 4 weeks

A tank contains 40 liters of a 20% salt solution. How much pure salt must be added to make a 30% salt solution in the tank?

• 4 liters

• 2 liters

• 10 liters

• 6 liters

A farmer has chickens and cows. If there are 20 animals in total and 56 legs, how many chickens and how many cows does the farmer have?

• 15 chickens and 5 cows

• 5 chickens and 15 cows

• 10 chickens and 10 cows

• 12 chickens and 8 cows

A boat travels upstream at 10 miles per hour and downstream at 15 miles per hour. If it takes 2 hours longer to travel upstream than downstream, how far did the boat travel?

• 30 miles

• 50 miles

• 40 miles

• 25 miles