Find the value of x if `0.08x+0.04y=10 and 0.2(x-1)+0 .4y=24.8`
A. 125
B. 150
C.1.25
D. 12.5

Options

A. B
B. D
C. C
D. A

Answer

To solve the equations \(0.08x + 0.04y = 10\) and \(0.2(x - 1) + 0.4y = 24.8\), we will follow these steps:

### Step 1: Write down the equations
We have the following two equations:
1. \(0.08x + 0.04y = 10\) (Equation 1)
2. \(0.2(x - 1) + 0.4y = 24.8\) (Equation 2)

### Step 2: Simplify Equation 2
First, we simplify Equation 2:
\[ 0.2(x - 1) + 0.4y = 24.8 \]
Distributing \(0.2\):
\[ 0.2x - 0.2 + 0.4y = 24.8 \]
Adding \(0.2\) to both sides:
\[ 0.2x + 0.4y = 24.8 + 0.2 \]
\[ 0.2x + 0.4y = 25 \] (Equation 2 simplified)

### Step 3: Eliminate \(y\)
Now we have:
1. \(0.08x + 0.04y = 10\) (Equation 1)
2. \(0.2x + 0.4y = 25\) (Equation 2 simplified)

To eliminate \(y\), we can multiply Equation 1 by \(10\) to make the coefficients of \(y\) the same:
\[ 10(0.08x + 0.04y) = 10(10) \]
This gives us:
\[ 0.8x + 0.4y = 100 \quad (Equation 3) \]

### Step 4: Subtract the equations
Now we have:
1. \(0.8x + 0.4y = 100\) (Equation 3)
2. \(0.2x + 0.4y = 25\) (Equation 2 simplified)

We can subtract Equation 2 from Equation 3:
\[ (0.8x + 0.4y) - (0.2x + 0.4y) = 100 - 25 \]
The \(y\) terms cancel out:
\[ 0.8x - 0.2x = 75 \]
\[ 0.6x = 75 \]

### Step 5: Solve for \(x\)
Now, divide both sides by \(0.6\):
\[ x = \frac{75}{0.6} \]
To eliminate the decimal, multiply the numerator and denominator by \(10\):
\[ x = \frac{750}{6} \]
Now, simplify:
\[ x = 125 \]

### Conclusion
The value of \(x\) is \(125\).