Question 6 - Figure it out - Page 145-147 - Chapter 6 Class 8 - Algebra Play (Ganita Prakash II)

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Question 6 A farm has some horses and hens. The total number of heads of these animals is 55 and the total number of legs is 150. How many horses and how many hens are on the farm? Can you solve this without letter-numbers? [Hint: If all the 55 animals were hens, then how many legs would there be? Using the difference between this number and 150, can you find the number of horses?]Let's follow the "Math Talk" hint and use simple logic instead of heavy algebra. Imagine every single one of those 55 animals is a hen. Since hens have 2 legs, there would be 55 × 2 = 110 legs But the farm actually has 150 legs! We are missing 40 legs (150 – 110 = 40) Where do those 40 extra legs come from? Horses! Every time you swap a hen out for a horse, you gain 2 legs (because horses have 4 legs, hens have 2). To get 40 extra legs, you need to swap in 20 horses (𝟒𝟎÷𝟐=𝟐𝟎). The Answer: There are 𝟐𝟎 horses. Since there are 55 animals total, there are 𝟑𝟓 hens ( 55−20=35 ).