the sum of two numbers is 59. the larger number is 23 more than the smaller number. what are the numbers?

18, 41

Step-by-step explanation:

simultaneous equation

x + y = 59

x - y = 23

subtract both equations

2y = 36

y = 18

x = 41

First, let's call the two numbers we are looking for:

Now, we can write:

(Equation 1) n+m=59

(Equation 2) n=m+23

first substitute n since it is (m+23)

(m+23) + m=59

m+23+m=59

2m+23=59

now subtract 23 from both sides since we want it to be zero in the left side

2m+23-23=59-23

2m=36

m=36/2=18

the smaller number is 18

now we can substitute 18 in the second equation

n=18+23=41

the bigger number is 41 and the smaller number is 18