Question

A class aquarium is in the same shape of a rectangular prism measuring 2ft x 1ft x 1.5ft. A large fish requires 212in^3 of space, and a small fish requires 114in^3. If the tank is to have exactly 30 fish, what is the maximum number of large fish the class can purchase?

Answer 1

This problem can be solved by optimization. Are you familiar with that?

Answer 2

Optimization is where you find the maximum/minimum of a function, by using its first derivative and stuff like that. Does that sound familiar? I can walk you through it.

Answer 3

It's quite simple really.

Answer 4

Wait...actually we can solve this by using simultaneous equations. Sorry about that.

Answer 5

Can you walk me through it please? i don't think i know how to do "optomization" or "stimultaneous equations" :O

Answer 6

Alright. We are going to use simultaneous equations. Now, letting the number of large fish be L and small fish be S, we can say that L+S=30, because that's the maximum number of fish that can be bought. right?

Answer 7

yupp

Answer 8

Nice. We can also say that 212L+114S=(2*1*1.5)=3, because that's the maximum volume of the aquarium. Right?

Answer 9

yes

Answer 10

So we have two simultaneous equations:
L+S=30
212L+114S=3
Are you with me till here?

Answer 11

yeah, so do i just get either L or S alone on the 1st equation and then plug it in on the 2nd equation?

Answer 12

Yep.

Answer 13

i got a decimal... L=8.25991

Answer 14

If you did the math right, that should be okay, and you'll thus round down the answer to 8 fish.

Answer 15

So do i plug L back into the equation or is 8 just the answer?

Answer 16

8 is the answer.

Answer 17

Thank you sooo much :D

Answer 18

You're welcome :)