The sum of two numbers is 40. the sum of the smaller and 5 times the larger is 144. find the numbers.

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! :)

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