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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineSteven and his cousin Carly are picking apples in their grandparents' orchard. Steven has filled 1515 baskets with apples and is filling them at a rate of 44 baskets per hour. Carly has 1111 full baskets and will continue picking at 88 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?\newlineIn ___\_\_\_ hours, the cousins will each have filled ___\_\_\_ baskets with apples.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineSteven and his cousin Carly are picking apples in their grandparents' orchard. Steven has filled 1515 baskets with apples and is filling them at a rate of 44 baskets per hour. Carly has 1111 full baskets and will continue picking at 88 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?\newlineIn ___\_\_\_ hours, the cousins will each have filled ___\_\_\_ baskets with apples.
  1. Define Variables: Let's define the variables:\newlineLet xx be the number of hours it takes for Steven and Carly to fill the same number of baskets.\newlineLet yy be the total number of baskets each has filled at that time.\newlineSteven's equation:\newlineSteven starts with 1515 baskets and fills them at a rate of 44 baskets per hour.\newliney=4x+15y = 4x + 15
  2. Steven's Equation: Carly's equation:\newlineCarly starts with 1111 baskets and fills them at a rate of 88 baskets per hour.\newliney=8x+11y = 8x + 11
  3. Carly's Equation: Now we have a system of equations:\newline11) y=4x+15y = 4x + 15\newline22) y=8x+11y = 8x + 11\newlineWe can use substitution to solve for xx by setting the two equations equal to each other since they both equal yy.\newline4x+15=8x+114x + 15 = 8x + 11
  4. System of Equations: Solve for xx:
    Subtract 4x4x from both sides:
    4x+15−4x=8x+11−4x4x + 15 - 4x = 8x + 11 - 4x
    15=4x+1115 = 4x + 11

    Subtract 1111 from both sides:
    15−11=4x+11−1115 - 11 = 4x + 11 - 11
    4=4x4 = 4x

    Divide both sides by 44:
    44=4x4\frac{4}{4} = \frac{4x}{4}
    1=x1 = x
  5. Solve for x: Now that we have the value of xx, we can substitute it back into either equation to find yy. We'll use Steven's equation:\newliney=4x+15y = 4x + 15\newliney=4(1)+15y = 4(1) + 15\newliney=4+15y = 4 + 15\newliney=19y = 19

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