Let's call the three numbers a, b, and c. Now we can turn the information we are given into equations. The sum of the three numbers is 26: a + b + c = 26 Twice the first (2 times a) minus the second (2 times a minus b) is 2 less than the third: 2a - b = c - 2 The third is the second minus three times the first: c = b - 3a Counting what we have here, we now have three equations and three variables: enough to solve the whole system of equations. The third equation gives us c directly, so we can start there and substitute into the second equation: 2a - b = (b - 3a) - 2 2a + 3a = b + b - 2 5a = 2b - 2 Let's get one of these variables on its own so we can continue with the substitution: 5a + 2 = 2b b = (5a + 2) / 2 Now we have c in terms of a and b, and b in terms of just a. So let's use the first equation and substitute to find out what a is: a + b + c = 26 a + (5a + 2) / 2 + (b - 3a) = 26 a + (5/2)a + 1 + (5a + 2) / 2 - 3a = 26 7/2a + 1 + 5/2a + 1 - 3a = 26 12/2a + 2 - 3a = 26 6a - 3a = 26 - 2 3a = 24 a = 8 At last, we have solved for one of the variables. Now, plug this into the equation for b to find b: b = (5a + 2) / 2 = (5(8) + 2) / 2 = (40 + 2) / 2 = 42 / 2 = 21 Now we have a and b. Time to find c! a + b + c = 26 (8) + (21) + c = 26 29 + c = 26 c = 26 - 29 c = -3 <span>So our values for a, b, and c are 8, 21, and -3.</span>
