Question

During a back-to-school shopping trip, a group of friends spent $245.86 on 14 shirts and pants. Each shirt cost $11.99. Each pair of pants cost $24.99. How many shirts and pairs of pants did the group buy?

a) Write a system of equations to model the information in the problem.
b) Study the system. Explain, without solving, which method you think would be most efficient for solving the system: substitution, elimination, graphing, or making a table. Explain why the other methods would be less efficient.
c) How could you simplify the numbers used in this system to simplify the system? Does this new system change your answers to part (b)? Explain.

Answer 1

a) Let x be the number of shirts and y be the number of pants.
We can create the following system of equations:
x + y = 14 (equation 1)
11.99x + 24.99y = 245.86 (equation 2)

b) To solve this system, substitution or elimination can be used. Graphing would be less efficient because it would be difficult to accurately graph the equations with decimal coefficients. Making a table would also be less efficient because it would require testing multiple values to find the solution.

c) To simplify the numbers used in the system, we can multiply both sides of equation 2 by 100 to remove the decimal coefficients. This would give us the following system:
x + y = 14 (equation 1)
1199x + 2499y = 24586 (equation 2)

This new system does not change the recommended method for solving (substitution or elimination) because we are only simplifying the coefficients, not changing the nature of the system.