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2 Mariam collects empty cans for recycling. She collects 3 cans on day 1, 6 cans on day 2, 12 cans on day 3, how many cans will she collect on day 6 if the pattern continues?

Mathematics

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Answers

2 parts
4.2

96 cans96 \text{ cans}

5.1

m=32,n=58m = 32, n = 58

Step-by-step solution

6 steps

Here are the solutions for both questions.

Part 4.2· 2 steps

  1. Identify the pattern in the number of cans collected.

    Day 1: 3 cans
    Day 2: 6 cans
    Day 3: 12 cans
    The number of cans collected doubles each day (3×2=63 \times 2 = 6, 6×2=126 \times 2 = 12).

  2. Extend the pattern using a table to find the number of cans on Day 6.

    DayCans
    13
    26
    312
    412×2=2412 \times 2 = 24
    524×2=4824 \times 2 = 48
    648×2=9648 \times 2 = 96

    Mariam will collect 96 cans on Day 6.

    The final answer for 4.2 is 96 cans\boxed{96 \text{ cans}}.

Part 5.1

m=32,n=58m = 32, n = 58

  1. Use the given equation y=x+7y = x + 7 to find the value of mm.

    From the table, when x=mx = m, the corresponding yy value is 39.
    Substitute these values into the equation:

    39=m+739 = m + 7
  2. Solve for mm.

    Subtract 7 from both sides of the equation:

    m=39−7m = 39 - 7 m=32m = 32
  3. Use the given equation y=x+7y = x + 7 to find the value of nn.

    From the table, when x=51x = 51, the corresponding yy value is nn.
    Substitute these values into the equation:

    n=51+7n = 51 + 7
  4. Solve for nn.

    Add the numbers:

    n=58n = 58

    The final answer for 5.1 is m=32,n=58\boxed{m = 32, n = 58}.

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