Page 120 - Start Up Mathematics_7

(c) Let the number be x. (d) Let Gaurav thinks of a number x.
3 3 11
On adding 3 to x, we get 21. He takes away 5 from x to get .
4
3 2 2
∴ x + 3 = 21 3 11
4 ∴ x – 5 = 2
2
3
⇒ x = 21 – 3 3 11
4 ⇒ x = + 5
3 2 2
⇒ x = 18
3
4 ⇒ x = 11 + 10
3 2 2
⇒ 4 × x = 18 × 4
3
4 ⇒ x = 21
⇒ 3x = 72 2 2
72 ⇒ 3x = 21
⇒ x =
3 ⇒ x = 21
⇒ x = 24 3
⇒ x = 7

Example 16: Solve the following:
(a) Sachin scored twice as many runs as Rahul. Together, their runs fell four short
of a century. How many runs did each one score?
(b) The second angle of a triangle is 15° less than twice the first angle. The third
angle is 20° more than the second angle. Find the three angles.
(c) The teacher tells the class that the highest marks obtained by a student in her
class is 15 less than thrice the lowest marks. The highest score is 96. What is
the lowest score?

(d) A man is 26 years older than his son. In five years, their ages will total 70. What
are their present ages?
Solution: (a) Let Rahul scored x runs.
∴ Sachin scored = 2x runs

x + 2x = 100 – 4
⇒ 3x = 96
96
⇒ x =
3
⇒ x = 32
∴ Rahul scored 32 runs and Sachin scored 2x = 64 runs.

(b) Let the first angle be x.
∴ the second angle = 2x – 15°
Now the third angle = (2x – 15°) + 20° = 2x + 5°

By angle sum property,
x + (2x – 15°) + (2x + 5°) = 180°
⇒ 5x – 10° = 180°

⇒ 5x = 190°
⇒ x = 38°

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