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

  1. Express c in terms of a and b

From the first equation, we have

$$ c = a + b $$

  1. Substitute c into the second equation

Now, substitute the expression for $c$ into the second equation $a + c = 22$:

$$ a + (a + b) = 22 $$

  1. Combine like terms

This simplifies to:

$$ 2a + b = 22 $$

  1. Isolate b

Now, solve for $b$:

$$ b = 22 - 2a $$

  1. 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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