Three times a number increased by five times another number is 49, but twice the second number exceeds five times the first number by 1. What are the numbers?

3   and   8

Explanation:

3a + 5b = 49

2b = 5a + 1

then:

2b - 5a = 1       equation 1

-5a + 2b = 1     equation 2

then:

multiplyng by -2.5 the equation 2 and sum to the equation 1:

   3a + 5b = 49

12.5a  - 5b = -2,5

15.5a  + 0   = 46.5

15.5a = 46.5

a = 46.5/15.5

a = 3

2b = 5a + 1

2b = (5*3) + 1

2b = 15 + 1

2b = 16

b = 16/2

b = 8

Check:

3a + 5b = 49

3*3 + 5*8 = 49

9 + 40 = 49

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