Exploring Linear Equations and Solutions in Math

1. Sarah has a budget of $50 to buy notebooks. Each notebook costs $5. If she buys 'x' notebooks, write an equation to represent her spending. How many notebooks can she buy if she spends all her money? Does this equation have one solution, no solution, or infinite solutions?

• 5 notebooks

• 15 notebooks

• 20 notebooks

• 10 notebooks

2. A school is planning a field trip and has a total of 120 students. If each bus can carry 30 students, write an equation to find the number of buses needed. What happens if the number of students changes to 150? Does the equation have one solution, no solution, or infinite solutions?

• The number of buses needed is 4 for 120 students and 5 for 150 students. The equation has one solution.

• The number of buses needed is 4 for 120 students and 6 for 150 students. The equation has two solutions.

• The number of buses needed is 3 for 120 students and 4 for 150 students. The equation has no solution.

• The number of buses needed is 5 for 120 students and 6 for 150 students. The equation has infinite solutions.

3. Tom and Jerry are saving money for a video game that costs $60. Tom saves $10 each week, while Jerry saves $15 each week. Write equations for their savings and determine if there is a week when they will have the same amount saved. Does this situation have one solution, no solution, or infinite solutions?

• Yes, they will have the same amount saved in week 4.

• Yes, there is a week (week 0) when they will have the same amount saved.

• Yes, they will have the same amount saved in week 2.

• No, they will never have the same amount saved.

4. A gardener is planting flowers in rows. If each row has the same number of flowers and there are 12 rows with a total of 48 flowers, write an equation to find the number of flowers per row. What if the total number of flowers changes to 0? Does this equation have one solution, no solution, or infinite solutions?

• 12; If total flowers = 0, the equation has two solutions.

• 4; If total flowers = 0, the equation has one solution (x = 0).

• 6; If total flowers = 0, the equation has infinite solutions.

• 3; If total flowers = 0, the equation has no solution.

5. A car rental company charges a flat fee of $20 plus $0.50 per mile driven. Write an equation for the total cost 'C' based on the number of miles 'm' driven. If a customer pays $20, how many miles did they drive? Does this situation have one solution, no solution, or infinite solutions?

• 10 miles

• 5 miles

• 15 miles

• 0 miles

7. A train travels at a constant speed of 60 miles per hour. Write an equation to represent the distance 'd' traveled in 't' hours. If the train travels for 0 hours, what is the distance? Does this equation have one solution, no solution, or infinite solutions?

• The distance is 120 miles and the equation has one solution.

• The distance is 0 miles and the equation has one solution.

• The distance is 60 miles and the equation has infinite solutions.

• The distance is 30 miles and the equation has no solution.

8. A store sells pencils for $0.50 each and erasers for $1.00 each. If a student buys 'x' pencils and 'y' erasers for a total of $10, write an equation to represent this situation. If the student buys only pencils, how many can they buy? Does this situation have one solution, no solution, or infinite solutions?

• The student can buy 25 pencils if they buy only pencils. This situation has no solution.

• The student can buy 20 pencils if they buy only pencils. This situation has infinite solutions.

• The student can buy 15 pencils if they buy only pencils. This situation has one solution.

• The student can buy 10 pencils if they buy only pencils. This situation has a unique solution.

9. A swimming pool is being filled with water at a rate of 5 gallons per minute. Write an equation to represent the total gallons 'g' after 't' minutes. If the pool is already full at 0 gallons, what does this mean for the solutions?

• g = 5t + 10, valid at t = 5

• g = 0, valid at t = 1

• g = 5t, with the solution only being valid at t = 0.

• g = 10t, valid for all t