Answer:
The marks that Brian get on the second test is 72
The marks that Brian get on the third test is 76
Explanation:
We have a question with a word problem
The parameters given are;
Average mark on three mathematics test = 78
The mark received on the first test, M₁ = 86
The average for the first two test = 3 + Mark received on the third test M₃
Let M₂ = The mark received on the second test
Therefore, we have three equations with three equations as follows;
(M₁ + M₂)/2 = 3 + M₃............. ...(1)
(M₁ + M₂ + M₃)/3 = 78.................(2)
M₁ = 86..........................................(3)
Which gives;
(86 + M₂)/2 = 3 + M₃............. ...(4)
(86 + M₂ + M₃)/3 = 78.................(5)
Making M₂ the subject of equation (4) gives;
M₂ = 2 × (3 + M₃) - 86
Replacing the value of M₂ in equation (5) gives;
(86 + (2 × (3 + M₃) - 86) + M₃)/3 = 78
(86 + (6 + 2·M₃) - 86) + M₃)/3 = 78
(6 + 2·M₃ + M₃)/3 = 78
6 + 3·M₃ = 78×3 = 234
3·M₃ = 234 - 6 = 228
M₃ = 228/3 = 76
From M₂ = 2 × (3 + M₃) - 86 = 6 + 2·M₃ - 86 = 2·M₃ - 80
We have;
M₂ = 2×76 - 80 = 72
Therefore, Brian got 72 on the second test and 76 on the third test.