Final answer:
By setting up equations based on Timothy and his brothers' lemonade stand transactions and solving them, it is determined that the cost of a cup of lemonade is $0.50.
Step-by-step explanation:
The question asks us to determine the cost of a cup of lemonade based on the purchases made by Paul and Nancy. Paul bought two cups of lemonade and two cookies for $3, and Nancy bought three cookies and two cups of lemonade for $4.00. To solve this problem, we can set up two equations to represent these transactions and use algebra to find the price of one cup of lemonade.
Let 'L' be the cost of one cup of lemonade and 'C' be the cost of one cookie. According to Paul's purchase, we have: 2L + 2C = $3.00. Nancy's purchase gives us: 3C + 2L = $4.00. By solving these two linear equations simultaneously, we can find the value of 'L'.
First, we need to isolate one variable. We can subtract the first equation from the second, which will give us C = $1.00. Now that we have the cost of a cookie, we can substitute it back into the first equation: 2L + 2($1.00) = $3.00, which simplifies to 2L = $1.00. Therefore, one cup of lemonade costs $0.50.