The length and width of a rectangular yard are 11 meters and 5 meters respectively. If each dimension were reduced by \( \times \) meters to make the ratio of length to width 8 to 3, what would be the value of \( x \) ?

Let's solve the problem step by step. **Given:** - Original length of the yard, \( L = 11 \) meters - Original width of the yard, \( W = 5 \) meters - Both dimensions are reduced by \( x \) meters - After reduction, the ratio of length to width is \( \frac{8}{3} \) **After Reduction:** - New length, \( L_{\text{new}} = 11 - x \) meters - New width, \( W_{\text{new}} = 5 - x \) meters **Setting Up the Equation:** \[ \frac{L_{\text{new}}}{W_{\text{new}}} = \frac{8}{3} \] \[ \frac{11 - x}{5 - x} = \frac{8}{3} \] **Cross-Multiplying to Solve for \( x \):** \[ 3(11 - x) = 8(5 - x) \] \[ 33 - 3x = 40 - 8x \] **Solving for \( x \):** 1. Add \( 8x \) to both sides: \[ 33 + 5x = 40 \] 2. Subtract \( 33 \) from both sides: \[ 5x = 7 \] 3. Divide both sides by \( 5 \): \[ x = \frac{7}{5} \text{ meters} \quad \text{or} \quad 1.4 \text{ meters} \] **Answer:** The value of \( x \) is \( \frac{7}{5} \) meters (or 1.4 meters).