The sum of three numbers is 95. The second number is 5 more than the first. The third number is 3 times the second. What are the numbers?
Prepare thyself for more questions.SquareOne said:Begin by turning the word problem into a system of equations:
Let \( x + y + z = 95 \), \( y = x + 5 \), and \( z = 3y \).
You can now use Elimination, Substitution, or Matrices to solve. I will use substitution by taking the 2nd and 3rd equations and getting the 1st equation in terms of \( y \).
\( y = x+ 5 \) subtract \( 5 \) from both sides.
\( x = y - 5 \)
Substitute \( x = y - 5 \) and \( z = 3y \) into \( x + y + z = 95 \):
\( ( y -5 ) + y + (3y) = 95 \) combine like terms
\( 5y - 5 = 95 \) add \( 5 \) to both sides
\( 5y = 100 \) divide by \( 5 \) on both sides
\( y = 20 \)
Substitute \( y = 20 \) into \( x = y - 5 \):
\( x = (20) - 5 \) simplify
\( x = 15 \)
Substitute \( y = 20 \) into \( z = 3y \):
\( z = 3(20) \) simplify
\( z = 60 \)
ANSWER: \( x = 15 \), \( y = 20 \), and \( z = 60 \)