Question 12 of 17intermediate🔧 ApplyNumerical4 marks

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?

Correct Answer

Given: Total heads = 55, Total legs = 150

Step 1: Let h = number of horses, c = number of hens

Step 2: From heads: h + c = 55 So c = 55 - h

Step 3: From legs: 4h + 2c = 150

Step 4: Substitute: 4h + 2(55 - h) = 150

Step 5: Simplify: 4h + 110 - 2h = 150 2h = 40 h = 20

Step 6: ∴ h = 20 horses, c = 35 hens

Answer: There are 20 horses and 35 hens on the farm.

Exercise: Figure it Out (Section 3) | Q: 6 | (Page Page 12)
For More Understanding

Explanation

Using algebra: Let h = horses, c = hens. Each has one head, so h + c = 55. Horses have 4 legs, hens have 2 legs, so 4h + 2c = 150. Solving: from first equation, c = 55 - h. Substituting: 4h + 2(55 - h) = 150, giving 2h = 40, so h = 20 and c = 35.

Solution Steps

  1. Step 1: Let h = number of horses, c = number of hens

  2. Step 2: From heads: h + c = 55, so c = 55 - h

  3. Step 3: From legs: 4h + 2c = 150

  4. Step 4: Substitute: 4h + 2(55 - h) = 150

  5. Step 5: Simplify: 4h + 110 - 2h = 150, so 2h = 40

  6. Step 6: Therefore h = 20 horses, c = 35 hens

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