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The larger of two numbers is five less than four times the smaller and the sum of two times the larger and four times the smaller is 74. What are the numbers?

The larger of two numbers is five less than four times the smaller and the sum of two times the larger and four times the smaller is 74. What are the numbers? Correct Answer 23 and 7

Calculation:

Let the number be a and b (a > b)

According to the question

a = 4b – 5      ----(1)

2a + 4b = 74      ----(2)

Putting value of a form equation (1) in equation (2), we get:

2(4b – 5) + 4b = 74

⇒ 8b – 10 + 4b = 74

⇒ 12b = 74 + 10

⇒ 12b = 84

⇒ b = 84/12 = 7

Putting value of b in equation (1)

a = 4 × 7 – 5

⇒ a = 28 – 5 = 23

∴ The numbers are 23 and 7

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