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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Steven and his cousin Carly are picking apples in their grand parents' orchard. Steven has filled baskets with apples and is filling them at a rate of baskets per hour. Carly has full baskets and will continue picking at baskets per hour. Once the cousins get to the point where they have filled the same number of baskets, they will carry them to the barn and then eat lunch. How long will that take? How much fruit will they have picked by then?In hours, the cousins will each have filled baskets with apples.
Full solution
Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Steven and his cousin Carly are picking apples in their grand parents' orchard. Steven has filled baskets with apples and is filling them at a rate of baskets per hour. Carly has full baskets and will continue picking at baskets per hour. Once the cousins get to the point where they have filled the same number of baskets, they will carry them to the barn and then eat lunch. How long will that take? How much fruit will they have picked by then?In hours, the cousins will each have filled baskets with apples.
- Define Variables: Define the variables for the number of baskets Steven and Carly have initially and their rates of filling baskets.Steven's initial baskets: Steven's rate: baskets/hourCarly's initial baskets: Carly's rate: baskets/hour
- Write Equations: Write the equations for the total number of baskets filled by Steven and Carly over time.Let represent the number of hours passed.Total baskets filled by Steven = (Rate of Steven Time) + Initial baskets of StevenTotal baskets filled by Carly = (Rate of Carly Time) + Initial baskets of CarlyFor Steven: For Carly:
- Substitution to Solve: Use substitution to solve for by setting the two equations equal to each other since they will have filled the same number of baskets.
- Solve for x: Solve for x.
- Find Total Baskets: Use the value of to find the total number of baskets filled by each cousin.
- Verify Solution: Verify the solution by plugging into Carly's equation.
- Answer Prompt: Answer the question prompt with the values obtained.In hours, the cousins will each have filled baskets with apples.
