There are two numbers whose sum is 64. The larger number subtracted from 4 times the smaller number gives 31. Find the numbers.

There are two numbers whose sum is 64. The larger number subtracted from 4 times the smaller number gives 31. Then the numbers are 45 and 19Solution:Given that, There are two numbers whose sum is 64.  Let the number be a and b in which a is bigger. Then, a + b = 64 ------ eqn (1) The larger number subtracted from 4 times the smaller number gives 31.  4 x b – a = 31  4b – a = 31 ----- eqn (2) We have to find the numbers. So, from eqn (2)a = 4b – 31Subatitute a in (1) 4b – 31 + b = 64 On solving we get5b  = 64 + 31  5b = 95b = 19 So, b = 19, then eqn 1a + 19 = 64On simplification,a = 64 – 19a = 45  Hence, the two numbers are 45 and 19