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4 August, 02:08

A report card has six marks. The average of the first and second marks is 72%. The average of

the second and third marks is 75%. The average of the third and fourth marks is 77%. The

average of the fourth and fifth marks is 78%. The average of the fifth and sixth marks is 79%.

a) Determine the overall average. b) Determine the average of the first and sixth marks.

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  1. 4 August, 02:34
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    a) Overall average = 76%

    b) Average of first and sixth marks = 75%

    Step-by-step explanation:

    Let's call the marks a, b, c, d, e and f, in this order.

    Then, we can write the following equations:

    (a+b) / 2 = 0.72 - > a + b = 1.44 (eq1)

    (b+c) / 2 = 0.75 - > b + c = 1.5 (eq2)

    (c+d) / 2 = 0.77 - > c + d = 1.54 (eq3)

    (d+e) / 2 = 0.78 - > d + e = 1.56 (eq4)

    (e+f) / 2 = 0.79 - > e + f = 1.58 (eq5)

    If we sum all equations, we have:

    a + 2b + 2c + 2d + 2e = f = 7.62 (eq6)

    Then, we make (eq6) - (eq2) - (eq4):

    a + b + c + d + e + f = 4.56 (eq7)

    a) The find the overall average, we just need to divide (eq7) by 6:

    Overall average = (a + b + c + d + e + f) / 6 = 0.76 = 76%

    b) First we need to make (eq7) - (eq2) - (eq4):

    a + f = 1.5

    Then, the average is:

    Average = (a+f) / 2 = 0.75 = 75%
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