If the mean of the following numbers is 17, find the c value. Produce an algebraic solution. Guess and check is unacceptable. 12, 18, 21, c, 13

The mean of a set of numbers is found by adding up all the numbers and dividing by the count of numbers present. For the given set of numbers, which includes 5 values (12, 18, 21, c, 13), the mean is: \[\text{Mean} = \frac{12 + 18 + 21 + c + 13}{5}\] You mentioned that the mean is 17. So, we can set up an equation using this information: \[\frac{12 + 18 + 21 + c + 13}{5} = 17\] Now, let's solve this equation to find the value of \(c\): \[12 + 18 + 21 + c + 13 = 5 \times 17\] \[64 + c = 85\] \[c = 85 - 64\] \[c = 21\] Therefore, the value of \(c\) that would make the mean of the set equal to 17 is \(c = 21\).