Question 42 of 60advanced🔍 AnalyzeNumerical4 marks

Sofia has only ₹50 and ₹20 notes. She needs to pay ₹520 using these notes. How many ₹50 and ₹20 notes does she need to make ₹520? Find out the different possible combinations.

Correct Answer

Formula: 50x + 20y = 520 (where x = number of ₹50 notes, y = number of ₹20 notes)

(1) If x = 10: 500 + 20y = 520 y = 1 ∴ 10 notes of ₹50 and 1 note of ₹20 = ₹520

(2) If x = 8: 400 + 20y = 520 y = 6 ∴ 8 notes of ₹50 and 6 notes of ₹20 = ₹520

(3) If x = 6: 300 + 20y = 520 y = 11 ∴ 6 notes of ₹50 and 11 notes of ₹20 = ₹520

(4) If x = 4: 200 + 20y = 520 y = 16 ∴ 4 notes of ₹50 and 16 notes of ₹20 = ₹520

(5) If x = 2: 100 + 20y = 520 y = 21 ∴ 2 notes of ₹50 and 21 notes of ₹20 = ₹520

Answer: The possible combinations are: (1) 10 notes of ₹50 and 1 note of ₹20 (2) 8 notes of ₹50 and 6 notes of ₹20 (3) 6 notes of ₹50 and 11 notes of ₹20 (4) 4 notes of ₹50 and 16 notes of ₹20 (5) 2 notes of ₹50 and 21 notes of ₹20

Exercise: Let Us Solve | Q: 3 | (Chapter: Page 8)
For More Understanding

Explanation

We need to find combinations where 50x + 20y = 520, where x is the number of ₹50 notes and y is the number of ₹20 notes. Testing values: If x = 10, then 50(10) = 500, remaining = 20, so y = 1. If x = 8, then 50(8) = 400, remaining = 120, so y = 6. If x = 6, then 50(6) = 300, remaining = 220, so y = 11. If x = 4, then 50(4) = 200, remaining = 320, so y = 16. If x = 2, then 50(2) = 100, remaining = 420, so y = 21.

Solution Steps

  1. Step 1: Equation: 50x + 20y = 520

  2. Step 2: If x = 10: 500 + 20y = 520, y = 1

  3. Step 3: If x = 8: 400 + 20y = 520, y = 6

  4. Step 4: If x = 6: 300 + 20y = 520, y = 11

  5. Step 5: If x = 4: 200 + 20y = 520, y = 16

  6. Step 6: If x = 2: 100 + 20y = 520, y = 21

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