Question 21

Fill in the blanks to make the statement true.
In a test, Abha gets twice the marks as that of Palak. Two times Abha's marks and three times Palak's marks make 280.

(a) If Palak gets x marks, Abha gets ............ marks.
(b) The equation formed is ...........
(c) The solution of the equation is ..........
(d) Marks obtained by Abha are ...........

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Solution

(a) If Palak gets x marks, then Abha gets twice the marks as that of Palak, i.e. 2x.

(b) Two times of Abha's marks = 2(2x) = 4x and three times the Palak marks = 3(x) = 3x
Now, two times Abha's marks and three times Palak's marks make 280.
So, the equation formed is 4x + 3x = 280.

(c) Solve the equation for x,
$\Rightarrow 4 x + 3 x = 280 \Rightarrow 7 x = 280 \Rightarrow \frac{7 x}{7} = \frac{280}{7} x = 40$
Hence, the solution of the equation is 40.

(d) Marks obtained by Abha are 2x, i.e. $2 \times 40 = 80.$

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