x= smaller number
y= larger number
EQUATION 1:
the sum of two numbers is 40
x + y= 40
EQUATION 2:
the sum of the first number and 5 times the second is 144
x + 5y= 144
STEP 1:
Solve for one variable in equation 1.
x + y= 40
subtract y from both sides
x= 40-y
STEP 2:
Substitute x=40-y in equation 2.
x + 5y= 144
(40-y) + 5y= 144
combine like terms
40 + 4y = 144
subtract 40 from both sides
4y= 104
divide both sides by 4
y= 26 larger number
STEP 3:
Substitute y=26 in either equation to solve for x (smaller number).
x + 5y= 144
x + 5(26)= 144
x + 130= 144
x= 14 smaller number
CHECK:
14 + 26= 40
40= 40
ANSWER: The smaller number is 14 and the larger number is 26.
Hope this helps! :)
