A fish has a head 9 long The tail is equal to the size of the head plus one-half the size of the body The body is the size of the head plus the tail How long is the fish?

Step 1: Define the variables: H = Head; T = Tail; B = Body Step 2: Set up equations from what is given in the problem: H = 9 T = H + 1/2B B = H + T Total Length of the Fish = H + T + B Step 3: Substitute between equations. If we know H = 9 then we can substitute 9 in for H in the second equation. T = 9 + 1/2B Now we know what T and H are, so lets substitute that into the third equation and solve for B. B = H + T B = 9 + (9 + 1/2B) B = 18 + 1/2B Then subtract 1/2B from both sides: 1/2B = 18 Multiply both sides by two: B = 36 Now we know the value of B and the value of H. Substitute this back into the second equation and solve for T. T = H + 1/2B T = 9 + (1/2)36 T = 9 + 18 = 27 Step 4: Plug all values of H, T, and B into the final equation. Total length of fish = H + T + B Total length of fish = 9 +27 + 36 = 72