If a + b = c and a + c = 22, what is b?
Understand the Problem
The question is asking to solve for the value of b given the equations a + b = c and a + c = 22. We can use the first equation to express c in terms of a and b, and then substitute into the second equation to find the value of b.
Answer
\( b = 22 - 2a \)
Answer for screen readers
The value of ( b ) can be expressed as ( b = 22 - 2a ).
Steps to Solve
- Express c in terms of a and b
From the first equation, we have
$$ c = a + b $$
- Substitute c into the second equation
Now, substitute the expression for $c$ into the second equation $a + c = 22$:
$$ a + (a + b) = 22 $$
- Combine like terms
This simplifies to:
$$ 2a + b = 22 $$
- Isolate b
Now, solve for $b$:
$$ b = 22 - 2a $$
- Final expression for b
We find that the value of $b$ can be expressed in terms of $a$ as follows:
$$ b = 22 - 2a $$
The value of ( b ) can be expressed as ( b = 22 - 2a ).
More Information
This expression indicates that the value of ( b ) depends on the choice of ( a ). For different values of ( a ), there will be corresponding values of ( b ). For example, if ( a = 5 ), then ( b = 22 - 2(5) = 12 ).
Tips
- Not substituting correctly: It's important to make sure that when you substitute ( c ) into the second equation, you do it accurately to avoid mistakes in algebraic manipulation.
- Forgetting to combine like terms: Remember to combine terms properly to simplify the equation before isolating a variable.
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