Solving and Graphing Linear Equations: Real-World Problems

A store sells pencils for $0.50 each and erasers for $0.75 each. If a student buys a total of 10 items for $6.00, how many pencils and erasers did they buy? Is there one solution, no solution, or infinite solutions?

• 5 pencils and 5 erasers

• 4 pencils and 6 erasers

• 7 pencils and 3 erasers

• 6 pencils and 4 erasers

Two friends are jogging on parallel paths. One jogs at a speed of 4 miles per hour, and the other jogs at 6 miles per hour. If they start at the same point, will they ever meet? Explain your reasoning using a graph.

• Yes, they will meet after a certain distance.

• They will meet at the halfway point.

• No, they will never meet.

• They will meet if they change their speeds.

A farmer has a rectangular field with a perimeter of 100 meters. If the length is twice the width, what are the dimensions of the field? Is there one solution, no solution, or infinite solutions?

• Width: 20 meters, Length: 40 meters

• Width: 16.67 meters, Length: 33.33 meters

• Width: 25 meters, Length: 50 meters

• Width: 10 meters, Length: 20 meters

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer pays $50, how many miles did they drive? Is there one solution, no solution, or infinite solutions?

• 75 miles

• 120 miles

• 100 miles

• 50 miles

Two equations are given: y = 2x + 3 and y = 2x - 1. Do these lines intersect? If so, how many solutions do they have? Graph the equations to support your answer.

• Yes, the lines are identical and have infinite solutions.

• No, the lines intersect at two points.

• No, the lines do not intersect and have no solutions.

• Yes, the lines intersect at one point.

A local bakery sells cupcakes for $2 each and cookies for $1 each. If a customer buys a total of 15 items for $24, how many cupcakes and cookies did they buy? Is there one solution, no solution, or infinite solutions?

• 9 cupcakes and 6 cookies

• 8 cupcakes and 7 cookies

• 7 cupcakes and 8 cookies

• 10 cupcakes and 5 cookies

A train travels at a constant speed of 60 miles per hour. If another train travels at 90 miles per hour, will they ever meet if they start from the same station at the same time? Explain your reasoning using a graph.

• No, they will never meet.

• They will meet if the faster train slows down.

• Yes, they will meet after a certain distance.

• They will meet at the halfway point between the two speeds.

A student is solving the equation 3x + 5 = 2x + 10. What is the solution to this equation? Is there one solution, no solution, or infinite solutions?

• One solution: x = 5

• No solution: x = 0

• One solution: x = 3

• Infinite solutions: x = 2x