Question

I am thinking of two numbers whose difference is 32. Twice the smaller number is 12 more than the larger number. What are my numbers?

Answer 1

Answer:
Smaller number = 44
Larger number = 76
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