SOLUTION: The difference of two numbers is 27. The second is 1 less than 3 times the first. What are the two numbers?

Question 44440This question is from textbook Begining Algebra
: The difference of two numbers is 27. The second is 1 less than 3 times the first. What are the two numbers? This question is from textbook Begining Algebra

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
You can write the necessary equations right from the problem:
Let the two numbers be x (the first number) and y (the second number).
x - y = 27 The difference of two numbers is 27.
y = 3x-1 The second is 1 less than three times the first. Substitute this into the first equation and solve for x.
x - (3x-1) = 27
x - 3x + 1 = 27 Collect like-terms.
-2x + 1 = 27 Subtract 1 form both sides.
-2x = 26 Divide both sides by -2.
x = -13
y = 3x-1
y = 3(-13)-1
y = -39-1
y = -40
Check:
x-y
-13-(-40) = -13 + 40 = 27
y = 3x-1
-40 = 3(-13)-1
-40 = -39-1
-40 = -40

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