\[ p+g=2.5 \] \( 1.58 p+1.09 g=3.46 \) What is the total number of pounds of peaches and grapefruit that Juan buys?

To solve the system of equations, we can start by expressing one variable in terms of the other. From the first equation: \[ g = 2.5 - p \] Now we can substitute \( g \) into the second equation: \[ 1.58 p + 1.09(2.5 - p) = 3.46 \] Expanding this gives: \[ 1.58 p + 2.725 - 1.09 p = 3.46 \] Combining like terms: \[ 0.49 p + 2.725 = 3.46 \] Now, isolate \( p \): \[ 0.49 p = 3.46 - 2.725 \] \[ 0.49 p = 0.735 \] \[ p = \frac{0.735}{0.49} \] \[ p \approx 1.5 \] Now, plug \( p \) back into the first equation to find \( g \): \[ g = 2.5 - 1.5 = 1.0 \] So, Juan buys approximately 1.5 pounds of peaches and 1.0 pound of grapefruit. To find the total number of pounds: \[ \text{Total} = p + g = 1.5 + 1.0 = 2.5 \] Thus, the total number of pounds of peaches and grapefruit that Juan buys is **2.5 pounds**.