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Twice the larger of two numbers is three more than five times the smaller and the sum of four times the larger and three times the smaller is 71. What are the numbers?

Twice the larger of two numbers is three more than five times the smaller and the sum of four times the larger and three times the smaller is 71. What are the numbers? Correct Answer 14, 5

Calculation:

Let the larger number be a and the smaller number be b.

2a = 5b + 3

2a – 5b = 3        ----(1)

4a + 3b = 71        ----(2)

Multiply the equation (1) by 2 and then subtract the equation (1) from equation (2),

4a – 10b = 6

4a – 4a + 3b – (-10b) = 71 – 6

3b + 10b = 65

13b = 65

b = 5

Using equation (1),

2a – 5 × 5 = 3

2a = 25 + 3 = 28

a = 14

∴ The numbers are 14 and 5.

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