Tim earned $300 in five days. After the first day, he earned $10 more each day than the day before. How much did Tim earn on the first day?

Question

Tim earned $300 in five days. After the first day, he earned $10 more each day than the day before. How much did Tim earn on the first day?

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    0
    2021-10-14T00:39:00+00:00

    Use the equation 300⇒5x to find how much tim made each day on average. 
    x⇒60   so, Day 1: $60, Day 2: $70 etc.. so the equation 300=5x+10 suffices the problem. 300⇒5x+10 ⇒    290=5x
    x=58
    So, Tim earned $58 his first day. Hope this helped.

    0
    2021-10-14T00:39:40+00:00

    The given problem is based on arithmetic sequence
    Sn = 300 (the sum of money in five days)
    d = 10 (the difference day by day)
    n = 5
    The question asks how much Tim earn on the first day, we write it as a₁

    The general formula to find the sum of a sequence is
    n/2 (2a₁ + d(n-1)) = Sn

    Input the numbers to the formula to find the value of a₁
    n/2 (2a₁ + d(n-1)) = Sn
    5/2 (2a₁ + 10(5-1)) = 300
    5/2 (2a₁ + 10(4)) = 300
    5/2 (2a₁ + 40) = 300
    2a₁ + 40 = 300 × 2/5
    2a₁ + 40 = 120
    2a₁ = 120 – 40
    2a₁ = 80
      a₁ = 80/2
      a₁ = 40

    The first day, Tim earned $40

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