Question 20 - Figure it out - Page 185 to 189 - Chapter 7 Class 7 - Finding the Unknown (Ganita Prakash II)

Transcript

Question 20 There are some children and donkeys on a beach. Together they have 28 heads and 80 feet. How many donkeys are there? How many children are there? Let Number of children = c Number of donkey = d Now, Children have 2 feet, and 1 head Donkey has 4 feet, and 1 head Given that Number of heads = 28 Number of children + Number of donkey = 28 c + d = 28 d = 28 – c Also, Number of feet = 80 2 × Number of children + 4 × Number of donkey = 80 2 × c + 4 × Number of donkey = 80 Putting Number of donkey = d = 28 – c 2 × c + 4 × (28 – c) = 80 2c + 4(28 – c) = 80 Solving the equation 2c + 4(28 – c) = 80 2c + 4 × 28 – 4c = 80 2c + 112 – 4c = 80 (2c – 4c) + 112 = 80 (–4c + 2c) + 112 = 80 –(4c – 2c) + 112 = 80 –2c + 112 = 80 Putting 112 on right side, it becomes –112 –2c = 80 – 112 –2c = –112 + 80 –2c = –(112 – 80) –2c = –32 Putting –2 on right side, so it becomes division Note: –2 doen’t become +2 on right side, since it is dividing c = (−𝟑𝟐)/(−𝟐) c = 32/2 c = 16 Thus, Number of children = c = 16 Number of donkeys = d = 28 – c = 28 – 16 = 12