When three numbers are added two at a time the sums are 29, 46, and 53. What is the sum of all three numbers?
I want to find three numbers x, y, and z that satisfy the equations x + y = 29, y + z = 46, and x + z = 53. I could try to solve this system of equations using elimination or substitution, but I notice that there is a simpler way to find the sum of all three numbers. If I add up all three equations, I get 2x + 2y + 2z = 128. This means that x + y + z = 64, which is the answer I'm looking for.

