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Linear Inequations (p-2) — Maths (commerce) STD 11 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Linear Inequations (p-2)2 Marks
Question
Rajiv obtained 70 and 75 marks in the first two unit tests. Find the minimum marks he should get in the third test to have an average of at least 60 marks.
✓

Answer

Let $x_1, x_2, x_3$ denote the marks in 1st, 2 nd and 3 rd unit test respectively. Then
$
\begin{aligned}
& \frac{x_1+x_2+x_3}{3} \geq 60 \\
& \therefore \frac{70+75+x_3}{3} \geq 60 \\
& \therefore 145+\mathrm{x}_3 \geq 3(60)
\end{aligned}
$
Subtracting 145 from both sides, we get
$
\begin{aligned}
& x_3 \geq 180-145 \\
& \therefore x_3 \geq 35
\end{aligned}
$
Rajiv must obtain a minimum of 35 marks to maintain an average of at least 60 marks.

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