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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.A group of friends are at a baseball game and are purchasing souvenirs. Dean purchased t-shirts and baseball caps, spending a total of . His Jonathan purchased t-shirts and baseball caps, which cost him a total of . Assuming that all of the t-shirts and all of the caps are the same price, what is the price of each?Shirts are _____ apiece and caps are _____ apiece.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.A group of friends are at a baseball game and are purchasing souvenirs. Dean purchased t-shirts and baseball caps, spending a total of . His Jonathan purchased t-shirts and baseball caps, which cost him a total of . Assuming that all of the t-shirts and all of the caps are the same price, what is the price of each?Shirts are _____ apiece and caps are _____ apiece.
- Define Variables: Let's denote the price of a t-shirt as and the price of a baseball cap as . We need to set up two equations based on the information given.Dean's purchase: + = Jonathan's purchase: + =
- Translate Purchases into Equations: Translate the purchases into equations.For Dean: For Jonathan:
- Solve System of Equations: We now have a system of equations:We can solve this system using the method of elimination or substitution. Let's use elimination to solve for one of the variables.
- Eliminate Variable 'c': Subtract the second equation from the first to eliminate 'c'.
- Find Value of 't': Now that we have the value of ' extit{t}', we can substitute it back into one of the original equations to find the value of ' extit{c}'.Using the second equation: Substitute :
- Substitute and Solve for 'c': Solve for 'c'.
