Desmond has a total of 15 fish. He has 3 more black fish than orange fish. How many orange fish does he have ?

Question

DESMOND HAS A TOTALOF 15 FISH. He HAS 3 MORE BLACK FISH THAN ORANGE FISH. hOW MANY ORANGE FISH DO HE HAVE /

Answer 1

Hi Mary,

 

 

I always used to get tripped up on these sorts of problems!  The technique that I find helpful is coming up with variables to stand in for the numbers that you don't know.

 

For instance, we could use the letter R to stand for the number of oRange fish Desmond has, and the letter B to stand for the number of Black fish (I picked R instead of O because O, the letter, and 0, the number, are too easy to confuse).

 

Now we can look and see what the problem tells us about R and B:

 

   R + B = 15 fish  (because Desmond has 15 fish total)

   R = B - 3 fish     (because there are 3 more black fish than orange fish)

 

Because R = B - 3 fish, we can substitute B - 3 fish for the R in the first equation, which gives us

 

   (B - 3 fish) + B = 15 fish

 

We can simplify this equation by adding the two Bs together, to get

 

   2B - 3 fish = 15 fish

 

adding 3 fish to each side,

 

   2B = 18 fish

 

and then dividing by 2:

 

   B = 9 fish

 

Now we know that Desmond has 9 Black fish... But we aren't done yet!  Remember that we want to know how many oRange fish Desmond has, so we need to use what we know about B to calculate R.

 

This is easy, though, since we already know that B - 3 fish = R (that Desmond has 3 more black fish than orange fish), so we just need to subtract 3 fish from B to get R.  This gives us

 

   R = 6 fish

 

FINALLY!  We have an answer: Desmond has 6 orange fish!  If you want to double-check, you can see that B + R does, in fact, equal 15 fish.

 

Like I said, these are really tricky problems, but once you figure out how to do them they're pretty fun.

 

 

I hope this is helpful!

Answer 2

Let x = the number of black fish and y = the number of orange fish.  We have two unknowns (x and y) so we need two equations relating the unknowns to find the answer.

 

Desmond has a total of 15 fish:  x + y = 15

 

He has three more black fish than orange fish: x = y + 3

 

Since x = y+3, let's substitute y+3 in place of x in the first equation and solve for y:

 

x + y = 15               [First equation]

y + 3 + y = 15        [Substituted y + 3 in place of x]

2y + 3 = 15

2y = 12

 

y = 6 orange fish