Troubleshooting: A=15-B, C=B+9, D=B+21

  • Context: MHB 
  • Thread starter Thread starter Ilikebugs
  • Start date Start date
  • Tags Tags
    Troubleshooting
Click For Summary
SUMMARY

The discussion focuses on solving a system of equations derived from the expressions A=15-B, C=B+9, and D=B+21. The equations are manipulated by multiplying each by 3 and summing them, leading to the conclusion that the average of the variables A, B, C, and D is 19.5. The calculations confirm that the total of A, B, C, and D equals 78, validating the average result. This systematic approach highlights the importance of algebraic manipulation in solving linear equations.

PREREQUISITES
  • Understanding of linear equations and systems of equations
  • Proficiency in algebraic manipulation techniques
  • Familiarity with average calculations in mathematics
  • Basic knowledge of mathematical notation and symbols
NEXT STEPS
  • Explore advanced techniques in solving systems of linear equations
  • Learn about matrix methods for solving linear equations
  • Study the implications of averages in statistical analysis
  • Investigate the use of algebra in real-world problem-solving scenarios
USEFUL FOR

Students, educators, and professionals in mathematics or related fields who are looking to enhance their understanding of algebraic systems and average calculations.

Ilikebugs
Messages
94
Reaction score
0
View attachment 6392 I know that its well above average.

So I got A= 15-B, C=B+9 and D=B+21, but I think I made a mistake somewhere
 

Attachments

  • Well.png
    Well.png
    23.6 KB · Views: 113
Mathematics news on Phys.org
Let's denote the four numbers by $a$, $b$, $c$ and $d$. Then we have the following system.
\[
\left\{
\begin{aligned}
a+\frac13b+\frac13c+\frac13d=25\\
\frac13a+b+\frac13c+\frac13d=37\\
\frac13a+\frac13b+c+\frac13d=43\\
\frac13a+\frac13b+\frac13c+d=51\\
\end{aligned}
\right.
\]
Multiply each equation by 3 and add them. Recall that you need to find $\dfrac{a+b+c+d}{4}$.
 
6(A+B+C+D)=468

(A+B+C+D)=78

Average is 19.5?
 
You are right.
 

Similar threads

MHB Solving Quadratic Equations with Binary Operator $\otimes$
  • · Replies 6 ·
Replies
6
Views
2K
MHB Find Solutions to a+b+c+d=4, a^2+b^2+c^2+d^2=6, a^3+b^3+c^3+d^3=94/9 in [0,2]
  • · Replies 2 ·
Replies
2
Views
1K
MHB Reflecting B(3,-1) on Line g: 4y + x - 15 = 0
  • · Replies 3 ·
Replies
3
Views
2K
MHB Find a,b,c,d for Max $a+b-c+d$
  • · Replies 1 ·
Replies
1
Views
1K
High School Commutative & Associative property of negative numbers
  • · Replies 4 ·
Replies
4
Views
3K
MHB (Seemingly) Random Sequences
  • · Replies 7 ·
Replies
7
Views
2K
MHB Prove $\sqrt{a}+\sqrt{b}+\sqrt{c}+\sqrt{d}\le 10$ w/ $a,b,c,d>0$
  • · Replies 5 ·
Replies
5
Views
2K
MHB Determine all possible values a/(a+b+d)+b/(a+b+c)+c/(b+c+d)+d/(a+c+d)
  • · Replies 2 ·
Replies
2
Views
2K
MHB -c5.LCM and Prime Factorization of A,B,C
  • · Replies 3 ·
Replies
3
Views
1K
MHB Solve for $d-b$: $a^5=b^4,\,c^3=d^2,\,c-a=19$
  • · Replies 1 ·
Replies
1
Views
1K