translate to a system of equations and solve

Question

the differnce between 2 numbers is 36 five times the largee is 11 times the smaller what are the numbers

Answer 1

Let the numbers be x, y in ascending order

the difference between 2 numbers is 36

(1) y - x = 36

five times the larger is 11 times the smaller

(2) 5y = 11x

rearrange (1) to get y = 36 + x

substitute in (2) to get 5(36 + x) = 11x

=> 180 + 5x = 11x

=> 180 = 6x

=> x = 30

substitute x value in (1) to get y - (30) = 36

=> y = 66

hence the two numbers are 30 and 66