There were 149 angelfish and goldfish in an aquarium. There were twice as many guppies as angelfish. After selling 35 goldfish, there are half as many goldfish as angelfish. How many fish are left in the aquarium?

guppies??

263

To solve this problem, we need to break it down into steps and use algebra to find the solution.

Step 1: Let's start by representing the number of angelfish as A.

Step 2: We are told that there were twice as many guppies as angelfish. So the number of guppies would be 2A.

Step 3: The problem states that there were 149 angelfish and goldfish combined. So the total number of fish in the aquarium can be written as A (number of angelfish) + G (number of guppies) + Gf (number of goldfish). This translates to:
A + 2A + Gf = 149.

Step 4: We also know that after selling 35 goldfish, there are half as many goldfish as angelfish left. We can represent this as: Gf - 35 = (1/2)A.

Step 5: Now we have two equations:
A + 2A + Gf = 149 and Gf - 35 = (1/2)A.

Step 6: Simplifying the second equation, we get: Gf = (1/2)A + 35.

Step 7: Substituting the value of Gf from the second equation into the first equation, we have:
A + 2A + ((1/2)A + 35) = 149.

Step 8: Combining like terms, we get: 5A/2 + 35 = 149.

Step 9: Solving for A, we subtract 35 from both sides: 5A/2 = 114.

Step 10: Then, multiply both sides by 2/5 to isolate A: A = (114 * 2)/5.

Step 11: Calculating the value of A, we find that A = 45.6.

Step 12: Since you can't have a fraction of a fish, we need to round down 45.6 to the nearest whole number, which is 45.

Step 13: Finally, substituting the value of A back into the second equation to find Gf: Gf = (1/2)*45 + 35 = 22.5 + 35 = 57.5.

Step 14: Similar to before, we round down 57.5 to the nearest whole number, which is 57.

Step 15: To find the number of guppies, we can substitute the value of A into the second equation: G = 2A = 2*45 = 90.

Step 16: To find the total number of fish left in the aquarium, we sum up the number of angelfish, guppies, and goldfish: A + G + Gf = 45 + 90 + 57 = 192.

Therefore, there are 192 fish left in the aquarium.