Verified answer

Let's make x the number of bears and y the number of dogs.

# of bears + # of dogs= 34

x + y = 34

amount bear eats + amount dogs eat = 36

.5x + 1.5y = 36

Your two equations right now are:

x + y = 34

.5x + 1.5y = 36

Find x by getting it on one side

x = 34 - y

Sub in for x in the second equation

.5(34-y) + 1.5y = 36

17 - 0.5y + 1.5y = 36

Solve for y

1y = 19

Therefore, there are 19 dogs. Now sub in the number of dogs into one of the equations.

x + 19 = 34

x = 15

You have 2 unknowns (how many bears and how many dogs) so you need 2 equations.

You know that there are 34 bears and dogs so your first equation is:

B+D=34

**I am not sure on the wording of average. If it means an average of 34 bears and 34 dogs your equation would be:

(B+D)/2 = 34

However, I think what the problem means is what I have originally for the first equation.

You also know that a dog eats 1.5 cans of food and a bear eats .5 cans for a total of 36 cans so your second equation is:

.5B + 1.5D = 36

Now that you have your two equations:

B+D=34

.5B + 1.5D = 36

Solve one to find B in terms of D:

B = 34 - D

Now, replace B in the second equation with what you just found:

.5(34 - D) + 1.5D = 36

Now solve for D:

D=19

Take this value and plug back into either equation to find B.

Does that make sense?

I think it is 36*.75=27 Dogs (.5 Bear), (.5 Dog) (.5 Dog) (.5 Dog)= 2 can food

36*.25=9 Bears

B = bears, D = dogs

B+D = 34 (in total of bears and dogs, there are 34 of them)

.5B + 1.5D = 36 (bear's food plus dog's food per day is 36)

B+D = 34

.5B + 1.5D = 36

multiply second equation by -2

B+D = 34

-B -3D = -72 Cancel out B's

__________

-2D = -38

D = 19

Plug D back to first equation

B + 19 = 34

B = 15

15 Bears and 19 Dogs

Let the no of dogs be X

No of bears = 34 - X

No of cans eaten per day = 1.5X + 0.5 ( 34 - X) = 36

1.5X + 17 - 0.5X = 36

X = 19

ANSWER 19 dogs and 15 bears

CHECK

19 X 1.5 = 28.5

15X 0.5 = 7.5

Total = 36 cans

1/2b+3/2d=36

1/2b+3/2(34-b)=36

multiply the whole equation by 2 then...

b+3(34-b)=72

simplify!

b+102-3b=72

simplify more

-2b+102=72

-102 -102

-2b=-30

divide by -2 on both sides

b=15

so there are 15 bears and 19 dogs