Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Mark and his cousin Leah are picking apples in their grandparents' orchard. Mark has filled 6 baskets with apples and is filling them at a rate of 4 baskets per hour. Leah has 12 full baskets and will continue picking at 3 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 much fruit will they have picked by then? How long will that take? Mark and Leah will each have filled _____ baskets in _____ hours.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  Mark and his cousin Leah are picking apples in their grandparents' orchard. Mark has filled 6 baskets with apples and is filling them at a rate of 4 baskets per hour. Leah has 12 full baskets and will continue picking at 3 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 much fruit will they have picked by then? How long will that take?   Mark and Leah will each have filled _____ baskets in _____ hours.

Bytelearn · Accepted Answer

Define Variables: Let's define the variables for the number of baskets Mark and Leah will have filled after a certain number of hours. Let x represent the number of hours that have passed since they started picking apples. Mark starts with 6 baskets and fills 4 baskets per hour, so the total number of baskets he will have filled after x hours is 6 + 4x. Leah starts with 12 baskets and fills 3 baskets per hour, so the total number of baskets she will have filled after x hours is 12 + 3x. We want to find the point where they have filled the same number of baskets, so we set the two expressions equal to each other to create the first equation of our system: 6 + 4x = 12 + 3xSet Up Equation: Now we need to solve for x. To do this, we will isolate x on one side of the equation. We can start by subtracting 3x from both sides to get rid of the x on the right side of the equation: 6 + 4x - 3x = 12 + 3x - 3x This simplifies to: 6 + x = 12Solve for x: Next, we subtract 6 from both sides to solve for x: 6 + x - 6 = 12 - 6 This simplifies to: x = 6 So, after 6 hours, they will have filled the same number of baskets.Calculate Mark's Baskets: Now we need to determine how many baskets each person will have filled after 6 hours. For Mark: 6 + 4x = 6 + 4(6) = 6 + 24 = 30 Mark will have filled 30 baskets.Calculate Leah's Baskets: For Leah: 12 + 3x = 12 + 3(6) = 12 + 18 = 30 Leah will also have filled 30 baskets.Final Answer: We have found that both Mark and Leah will have filled 30 baskets each after 6 hours. This answers the question prompt.

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