The weighted mean of marks in Mathematics, Science, and English is 82. The marks in Mathematics and Science are 76 and 88, with weights 3 and 4, respectively. If the weight of English is 3, find the marks in English.

Question: The weighted mean of marks in Mathematics, Science, and English is 82. The marks in Mathematics and Science are 76 and 88, with weights 3 and 4, respectively. If the weight of English is 3, find the marks in English.

Solution:
Given that,
Marks in Mathematics, x₁ = 76, Weight, w₁ = 3
Marks in Science, x₂ = 88, Weight, w₂ = 4
Weight of English, w₃ = 3
And weighted Mean = 82

Let the marks in English = x₃

We know,
Weighted Mean = [(w₁ × x₁) + (w₂ × x₂) + (w₃ × x₃)] ÷ (w₁ + w₂ + w₃)
82 = [(3 × 76) + (4 × 88) + (3 × x₃)] ÷ (3 + 4 + 3)
⇒ 82 = [228 + 352 + 3x₃] ÷ 10
⇒ 580 + 3x₃ = 82 × 10
⇒ 3x₃ = 820 - 580
⇒ 3x₃ = 240
⇒ x₃ = 240 ÷ 3
∴ x₃ = 80

So, the marks in English are 80.