Question

4
directions: type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s).
logan is buying equipment for the football team and the baseball team.
he spends $40 on football uniforms, and he plans on purchasing some footballs. logan uses this equation to show the total cost of football equipment, y, based on the number of footballs purchased, x.
\\( y = 40 + 10x \\)
logan also spends $200 on baseball uniforms, and he plans on purchasing some baseballs. logan uses this equation to show the total cost of baseball equipment, y, based on the number of baseballs purchased, x.
\\( y = 200 + 2x \\)
logan wants to spend the same amount of money on the football team and the baseball team, and he wants to purchase the same number of footballs and baseballs.
the coordinate pair that represents this solution is ( \\( \square \\) , \\( \square \\) ).

Explanation:

Step1: Set the two equations equal

Since the total cost \( y \) and the number of items \( x \) are the same for both teams, we set \( 40 + 10x = 200 + 2x \).

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 40 + 8x = 200 \).
Subtract 40 from both sides: \( 8x = 160 \).
Divide by 8: \( x = 20 \).

Step3: Find \( y \) using one equation

Substitute \( x = 20 \) into \( y = 40 + 10x \):
\( y = 40 + 10(20) = 40 + 200 = 240 \).

Answer:

(20, 240)