Question 19 of 19intermediate🔧 ApplyNumerical4 marks

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?

Correct Answer

Given: Let cc = number of children and dd = number of donkeys. Total heads = 28, Total feet = 80. Children have 1 head and 2 feet; donkeys have 1 head and 4 feet.

Equations: c+d=28c + d = 28 (heads) 2c+4d=802c + 4d = 80 (feet)

Solution: From the heads equation: c=28−dc = 28 - d Substituting into the feet equation:

2(28−d)+4d=802(28 - d) + 4d = 80 56−2d+4d=8056 - 2d + 4d = 80 56+2d=8056 + 2d = 80 2d=242d = 24 d=12d = 12 c=28−12=16c = 28 - 12 = 16

Answer: There are 12 donkeys and 16 children.

Verification: 12+16=2812 + 16 = 28 heads 12×4+16×2=48+32=8012 \times 4 + 16 \times 2 = 48 + 32 = 80 feet

Exercise: Figure it Out (Section 3) | Q: 20 | (Page Page 26)
For More Understanding

Explanation

Let cc = number of children and dd = number of donkeys. Children have 1 head and 2 feet; donkeys have 1 head and 4 feet. Equations: c+d=28c + d = 28 (heads) and 2c+4d=802c + 4d = 80 (feet). From the first equation: c=28−dc = 28 - d. Substituting: 2(28−d)+4d=802(28 - d) + 4d = 80, giving 56−2d+4d=8056 - 2d + 4d = 80, so 2d=242d = 24, d=12d = 12. Then c=16c = 16.

Solution Steps

  1. Step 1: Let cc = children, dd = donkeys

  2. Step 2: Heads equation: c+d=28c + d = 28

  3. Step 3: Feet equation: 2c+4d=802c + 4d = 80

  4. Step 4: From heads: c=28−dc = 28 - d

  5. Step 5: Substitute: 2(28−d)+4d=802(28 - d) + 4d = 80

  6. Step 6: Simplify: 56+2d=8056 + 2d = 80

  7. Step 7: 2d=242d = 24, d=12d = 12

  8. Step 8: c=28−12=16c = 28 - 12 = 16

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