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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. Emmy purchased t-shirt and baseball caps, spending a total of . Her Tanvi purchased t-shirts and baseball caps, which cost her 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. Emmy purchased t-shirt and baseball caps, spending a total of . Her Tanvi purchased t-shirts and baseball caps, which cost her 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.Emmy's purchase: t-shirt caps Tanvi's purchase: t-shirts caps
- Translate Purchases into Equations: Translate the purchases into equations.For Emmy: For Tanvi:
- Solve System of Equations: We now have a system of equations:We can solve this system using either substitution or elimination. Let's use the elimination method.
- Eliminate Variable 't': To eliminate one of the variables, we can multiply the first equation by to align the coefficients of 't' for subtraction.This gives us:
- Subtract Equations: Now we subtract the new equation from the second original equation to eliminate .
- Simplify Equation: Simplify the equation to solve for 'c'.Since we are trying to eliminate 't', we should not have 't' in this equation. There is a mistake here.
