Question

Solve the equation. Choose the method you prefer to use. Check your answer.
StartFraction b Over 9 EndFraction
plusone fourth
equals19

Answer 1

To solve the equation

\[
\frac{b}{9} + \frac{1}{4} = 19,
\]

we can start by isolating the term \(\frac{b}{9}\).

1. Subtract \(\frac{1}{4}\) from both sides:

\[
\frac{b}{9} = 19 - \frac{1}{4}.
\]

2. To combine the right side, we should have a common denominator. The common denominator between \(1\) and \(4\) is \(4\). Rewrite \(19\) as a fraction:

\[
19 = \frac{76}{4}.
\]

Now we can combine the fractions:

\[
19 - \frac{1}{4} = \frac{76}{4} - \frac{1}{4} = \frac{76 - 1}{4} = \frac{75}{4}.
\]

So we have:

\[
\frac{b}{9} = \frac{75}{4}.
\]

3. To solve for \(b\), multiply both sides by \(9\):

\[
b = 9 \cdot \frac{75}{4} = \frac{675}{4}.
\]

4. This can also be expressed as:

\[
b = 168.75.
\]

5. Now, let's check our solution by substituting \(b\) back into the original equation:

\[
\frac{675/4}{9} + \frac{1}{4}.
\]

Calculating \(\frac{675/4}{9}\):

\[
\frac{675}{4} \cdot \frac{1}{9} = \frac{675}{36} = \frac{75}{4}.
\]

Now substituting back into the equation:

\[
\frac{75}{4} + \frac{1}{4} = \frac{75 + 1}{4} = \frac{76}{4} = 19.
\]

Since both sides are equal, our solution is verified. Thus, the final answer is:

\[
b = \frac{675}{4} \text{ or } 168.75.
\]