Threee numbers,a, b, and c, have sum of 672. The value of a is 25% less than the sum of b and c. What is the value of a?

Options

A. `97`
B. `135`
C. `288`
D. `372`

Answer

To solve the problem step by step, let's break it down:

1. **Set up the equations**: We know that the sum of the three numbers \(a\), \(b\), and \(c\) is 672. Therefore, we can write the equation:
\[ a + b + c = 672 \]

2. **Express \(a\) in terms of \(b\) and \(c\)**: The problem states that \(a\) is 25% less than the sum of \(b\) and \(c\). This means:
\[ a = (b + c) - 0.25(b + c) = 0.75(b + c) \]

3. **Substitute \(b + c\)**: From the first equation, we can express \(b + c\) in terms of \(a\):
\[ b + c = 672 - a \]
Now substitute this into the equation for \(a\):
\[ a = 0.75(672 - a) \]

4. **Solve for \(a\)**: Distributing the 0.75 gives:
\[ a = 504 - 0.75a \]
Now, add \(0.75a\) to both sides to combine like terms:
\[ a + 0.75a = 504 \]
\[ 1.75a = 504 \]

5. **Isolate \(a\)**: Divide both sides by 1.75 to find \(a\):
\[ a = \frac{504}{1.75} \]

6. **Calculate the value of \(a\)**: Performing the division:
\[ a = 288 \]

Thus, the value of \(a\) is **288**.