The sum of two numbers is 17 and their difference is 29. What are the two numbers?

Question

Isaiah Anthony · Accepted Answer

See a solution process below:

First, let's give the two numbers a name: Number 1: we will call: #n# Number 2: we will call: #m# From the information in the problem we can write these two equations: Equation 1: #n + m = 17# Equation 2: #n - m = 29# Step 1 Solve the first equation for #n#: #n + m = 17# #n + m - color(red)(m) = 17 - color(red)(m)# #n + 0 = 17 - m# #n = 17 - m# Step 2 Substitute #(17 - m)# for #n# in the second equation and solve for #m#: #n - m = 29# becomes: #(17 - m) - m = 29# #17 - 1m - 1m = 29# #17 + (-1 - 1)m = 29# #17 + (-2)m = 29# #17 - 2m = 29# #-color(red)(17) + 17 - 2m = -color(red)(17) + 29# #0 - 2m = 12# #-2m = 12# #(-2m)/color(red)(-2) = 12/color(red)(-2)# #(color(red)(cancel(color(black)(-2)))m)/cancel(color(red)(-2)) = -6# #m = -6# Step 3 Substitute #-6# for #m# in the solution to the first equation at the end of Step 1 and calculate #n#: #n = 17 - m# becomes: #n = 17 - (-6)# #n = 17 + 6# #n = 23# The Two Numbers Are: #23# and #-6#

Jameson Allen · Answer

undefined The two numbers are -6 and 23.