M : n : 40 =5 : 20 : 10

To solve the proportion \( m : n : 40 = 5 : 20 : 10 \), we can set up the following equations based on the ratios given. From the ratio \( 5 : 20 : 10 \), we can write: - \( m = k \cdot 5 \) - \( n = k \cdot 20 \) - \( 40 = k \cdot 10 \) To find \( k \), we can solve the equation involving 40: \[ 40 = k \cdot 10 \\ k = \frac{40}{10} = 4 \] Now we can find \( m \) and \( n \): - \( m = 5k = 5 \cdot 4 = 20 \) - \( n = 20k = 20 \cdot 4 = 80 \) Thus, the values of \( m \) and \( n \) are \( m = 20 \) and \( n = 80 \). In summary: \[ m = 20, \; n = 80, \; 40 = 40 \]