To solve the equation
\[ \frac{9}{10}x + \frac{4}{5} = 28, \]
we can start by isolating \( x \).
- Subtract \( \frac{4}{5} \) from both sides:
\[ \frac{9}{10}x = 28 - \frac{4}{5}. \]
- To perform the subtraction, we need a common denominator. The common denominator for \( 28 \) (which is \( \frac{28 \cdot 5}{5} = \frac{140}{5}\)) and \( \frac{4}{5} \) is \( 5 \):
\[ 28 = \frac{140}{5}, \quad \text{thus,} \] \[ 28 - \frac{4}{5} = \frac{140}{5} - \frac{4}{5} = \frac{136}{5}. \]
So now the equation looks like this:
\[ \frac{9}{10}x = \frac{136}{5}. \]
- To get rid of the fraction, multiply both sides by \( \frac{10}{9} \):
\[ x = \frac{136}{5} \cdot \frac{10}{9}. \]
- Simplifying this:
\[ x = \frac{1360}{45}. \]
- Now let's reduce \( \frac{1360}{45} \):
- Factor both \( 1360 \) and \( 45 \):
- \( 1360 = 2^4 \times 5 \times 17 \)
- \( 45 = 3^2 \times 5 \)
The common factor is \( 5 \):
\[ x = \frac{1360 \div 5}{45 \div 5} = \frac{272}{9}. \]
Now we will compare this result with the options you provided:
- \( \frac{90}{4} = 22.5 \)
- \( \frac{133}{5} = 26.6 \)
- \( \frac{275}{9} \) (approximately 30.56)
- \( \frac{97}{3} \) (approximately 32.33)
Since \( \frac{272}{9} \approx 30.22 \) does not match any of your provided solutions either.
Let me check the calculation once more:
Returning to \( x = \frac{1360}{45} \):
\[ \frac{1360 \div 5}{45 \div 5} = \frac{272}{9}. \]
So the correct answer isn't available in the given options. The solution to the equation is \( x = \frac{272}{9} \).