(b) If \( a: b: c=5: 7: 3 \) and \( a+b=36 \), then find the value of \( : a, b \) and \( c \)
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To solve for the values of \( a, b, \) and \( c \) given the ratio \( a: b: c = 5: 7: 3 \) and the condition that \( a + b = 36 \), we can start by expressing \( a, b, \) and \( c \) in terms of a common variable. Let \( a = 5k \), \( b = 7k \), and \( c = 3k \) for some non-negative value \( k \). Now we can use the equation \( a + b = 36 \): \[ 5k + 7k = 36 \] \[ 12k = 36 \] \[ k = 3 \] Now substituting back to find \( a, b, \) and \( c \): \[ a = 5k = 5 \times 3 = 15 \] \[ b = 7k = 7 \times 3 = 21 \] \[ c = 3k = 3 \times 3 = 9 \] Thus, the values are: \[ a = 15, \, b = 21, \, c = 9 \]