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

  • Thread starter Thread starter adridgarcia
  • Start date Start date
  • Tags Tags
    Algebra Algebra 2
adridgarcia
Messages
1
Reaction score
0
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?
 
Mathematics news on Phys.org
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
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

MHB (Seemingly) Random Sequences
Replies
7
Views
2K
B What went wrong with (-x)^2=x^2?
Replies
22
Views
2K
MHB Cot (60°) = 1/tan (60°) = 1/sqrt{3}
Replies
2
Views
1K
I What is the role of geometry and dimensional operations?
Replies
3
Views
2K
B About a definition: What is the number of terms of a polynomial P(x)?
Replies
48
Views
3K
MHB Solve Inequality & Simul Eqns: Alg Workings Q (a,b,c)
Replies
1
Views
1K
MHB Show x³y+y³z+z³x is a constant
Replies
1
Views
1K
MHB What is the Sum of x, y, and z in a Non-Negative Real Number System?
Replies
4
Views
1K
A The abc conjecture and Virasoro algebra
Replies
1
Views
2K
I How to solve an equation with FMOD in it
Replies
10
Views
1K

Hot Threads

Recent Insights

Back
Top