Answer: Smaller number = 44 Larger number = 76 Step-by-step explanation: let x and y be the two numbers we are looking for and x ≤ y we must interpret the statement “their difference is 32” like this: y - x = 32 we must interpret the statement “Twice the smaller number is 12 more than the larger number” like this: 2x = y + 12
As a result we get this system of equations : y - x = 32 2x = y + 12 Let’s solve it (We proceed by elimination) : y - x = 32 2x = y + 12 ⇔ -x + y = 32 We label this Equation (1) 2x - y = 12 We label this Equation (2)
(1) + (2) → -x + y + 2x - y = 32 + 12 then x = 44 Now we replace x in equation (1) we get -44 + y = 32 then y = 32 + 44 = 76
