# Help? Algebra 2 Math - Solve X,Y,Z

• MHB
In summary, the sum of three numbers is 95, with the second number being 5 more than the first, and the third number being 3 times the second. The numbers are x=15, y=20, and z=60.

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?

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 $$z = 60$$

Beer soaked comment follows.
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 $$z = 60$$
Prepare thyself for more questions.
Spoon feeding can be very addictive.

jonah said:
Prepare thyself for more questions.
Spoon feeding can be very addictive.
Spoon feeding can be very "additive." (Dance)

-Dan