Graphing and Solving Linear Equations in Real-Life Scenarios

1. A school is selling tickets for a play. Adult tickets cost $10 and student tickets cost $5. If the school wants to raise $300, how many adult and student tickets should they sell? Graph the equations to find the solution.

• Sell 15 adult tickets and 30 student tickets.

• Sell 20 adult tickets and 10 student tickets.

• Sell 10 adult tickets and 40 student tickets.

• Sell 30 adult tickets and 0 student tickets, or 0 adult tickets and 60 student tickets.

2. Two friends, Alex and Jamie, are saving money for a concert. Alex saves $15 a week, while Jamie saves $10 a week. If Alex starts with $50 and Jamie starts with $30, how many weeks will it take for them to have the same amount of money? Solve and graph the equations.

• 8 weeks

• 2 weeks

• 4 weeks

• 6 weeks

3. A farmer has a total of 100 animals, consisting of cows and chickens. If cows are counted as 1 and chickens as 0.5, how many of each type of animal does the farmer have if the total count is 70? Set up the equations and graph them to find the solution.

• 40 cows and 60 chickens

• 20 cows and 80 chickens

• 50 cows and 50 chickens

• 30 cows and 70 chickens

4. A car rental company charges a flat fee of $20 plus $0.50 per mile driven. Another company charges a flat fee of $15 plus $0.75 per mile. How many miles must you drive for the costs to be the same? Solve and graph the equations to find the answer.

• 25 miles

• 20 miles

• 30 miles

• 15 miles

5. A local gym offers two membership plans. Plan A costs $30 per month, while Plan B has a one-time fee of $100 and $20 per month. After how many months will both plans cost the same? Solve the equations and graph them to find the solution.

• 5 months

• 15 months

• 12 months

• 10 months

6. A store sells two types of bicycles: mountain bikes for $200 and road bikes for $150. If a customer wants to spend exactly $600, how many of each type can they buy? Set up the equations and graph them to find the combinations.

• (2 mountain bikes, 2 road bikes)

• The combinations of bicycles are: (0 mountain bikes, 4 road bikes), (1 mountain bike, 2 road bikes), (2 mountain bikes, 0 road bikes).

• (4 mountain bikes, 0 road bikes)

• (3 mountain bikes, 1 road bike)

7. A restaurant sells two types of sandwiches: a veggie sandwich for $5 and a meat sandwich for $7. If a customer spends $40, how many of each type of sandwich can they buy? Solve the equations and graph them to find the possible combinations.

• Possible combinations: (0, 5), (1, 4), (2, 3), (3, 2), (4, 1), (5, 0)

• (0, 6)

• (2, 2)

• (3, 3)

8. A school is planning a field trip and has a budget of $500. The bus rental costs $200 and each student ticket costs $10. How many student tickets can they buy? Set up the equations and graph them to find the maximum number of tickets.

• 30

• 25

• 35

• 40

9. Two companies produce the same product. Company A produces 100 units at a cost of $5 each, while Company B produces 150 units at a cost of $4 each. How many units must each company produce to have the same total cost? Solve and graph the equations to find the solution.

• Company A must produce 120 units and Company B must produce 150 units.

• Company A must produce 80 units and Company B must produce 100 units.

• Company A must produce 90 units and Company B must produce 110 units.

• Company A must produce 100 units and Company B must produce 125 units.

10. A bookstore sells novels for $12 and textbooks for $20. If a customer wants to buy a total of 10 books and spend exactly $180, how many of each type can they buy? Set up the equations and graph them to find the answer.

• 4 novels and 6 textbooks

• 5 novels and 5 textbooks

• 2 novels and 8 textbooks

• 3 novels and 7 textbooks