Page 121 - Start Up Mathematics_7

Second angle = 2x – 15° = 2(38°) – 15° = 61°

Third angle = 2x + 5° = 2(38°) + 5° = 81°
Thus, the three angles of a triangle are 38°, 61° and 81°.

(c) Let the lowest marks obtained be x.

Since, the highest marks scored = 96
∴ 3x – 15 = 96

⇒ 3x = 96 + 15
⇒ 3x = 111

⇒ x = 37
Hence, the lowest marks scored = 37.

(d) Present ages:
Let son’s age be x years.
∴ Father’s age = x + 26
5 years hence:
Son’s age after 5 years = x + 5
Father’s age after 5 years = (x + 26) + 5 = x + 31
Now, (x + 5) + (x + 31) = 70
⇒ 2x + 36 = 70
⇒ 2x = 34
⇒ x = 17

Hence, the present age of the son is 17 years and the present age of the father
is 43 years.

Example 17: Solve the following:
(a) Maya, Madhura and Mohsina are friends studying in the same class. In a class
test in Geography, Maya got 16 out of 25 and Madhura got 20. The average
score of all the three was 19. How much did Mohsina score?
(b) The length of a rectangle is 4 cm less than thrice the width. When the length
is increased by 7 cm and the width is decreased by 2 cm, the perimeter equals
90 cm. Find the length and width of the rectangle.
Solution: (a) Maya’s score = 16
Madhura’s score = 20
Let the score of Mohsina be x.

 The average score = 19
16 + 20 + x
∴ = 19
3
⇒ 36 + x = 57
⇒ x = 57 – 36

⇒ x = 21
Hence, Mohsina’s score is 21.

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