solve for a, b, and c if a + b = 10 a + c = 20 b + c = 24 Hence solve for a + b + c

You can solve this system of equations using a technique called simultaneous equation solving. Let's start with the three equations you provided: a + b = 10 a + c = 20 b + c = 24 First, you can isolate 'a' in equation (1) by subtracting 'b' from both sides: a = 10 - b Now, substitute this expression for 'a' into equations (2) and (3): (10 - b) + c = 20 b + c = 24 Now, you have a system of two equations with two variables: 10 - b + c = 20 b + c = 24 Let's solve equation (2) for 'c': 10 - b + c = 20 Subtract 10 from both sides: c = 20 - 10 + b c = 10 + b Now, substitute this expression for 'c' into equation (3): b + (10 + b) = 24 Combine like terms: 2b + 10 = 24 Subtract 10 from both sides: 2b = 24 - 10 2b = 14 Now, divide both sides by 2 to solve for 'b': b = 14 / 2 b = 7 Now that you know 'b' is 7, you can find 'c' using the expression for 'c' you found earlier: c = 10 + b c = 10 + 7 c = 17 Now that you have found the values of 'b' and 'c', you can find 'a' using the expression for 'a' you found at the beginning: a = 10 - b a = 10 - 7 a = 3 So, you've found that: a = 3 b = 7 c = 17 To find a + b + c: a + b + c = 3 + 7 + 17 = 27 Therefore, a + b + c is equal to 27.