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