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

The average is 19.5. In summary, the conversation discusses solving a system of equations to find the average of four numbers, which is determined to be 19.5.
  • #1
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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
 

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  • #2
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 $\dfrac{a+b+c+d}{4}$.
 
  • #3
6(A+B+C+D)=468

(A+B+C+D)=78

Average is 19.5?
 
  • #4
You are right.
 

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

What do the variables A, B, C, and D represent in this equation?

The variables A, B, C, and D represent unknown values that can be solved for using the given equations. A, B, and C are related through addition and subtraction, while D is related to B through multiplication.

How do I solve for variable A in this equation?

To solve for A, you can substitute the given equations for C and D into the first equation. This will result in an equation that only has the variable B, which can then be solved for. Once the value of B is determined, it can be substituted back into the equations for C and D to find the value of A.

Can this equation be solved for more than one set of values?

Yes, as long as the equations are followed correctly, there can be multiple sets of values that satisfy the equations. This is because there are multiple unknown variables and not enough equations to uniquely determine each one.

What should I do if I get a negative value for one of the variables?

If you get a negative value for one of the variables, double check your calculations and make sure you followed the correct order of operations. You may also want to check if there are any restrictions on the values of the variables, such as being positive or integers only.

Can this equation be solved using different methods?

Yes, there are multiple methods that can be used to solve this equation, such as substitution, elimination, or graphing. The method you choose may depend on the specific problem and your personal preference.

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