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.

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%