Algebra 2 question?

Question

There are a total of 18 monkeys and orangutans in a primate habitat. The monkeys each eat 5 bananas a days, and the orangutans each eat 8 bananas a day. Each day, the monkeys and orangutans together eat a total of 111 bananas. How many monkeys and orangutans are in the habitat?

 

A) 10 monkeys and 8 orangutans

B) 11 monkeys and 7 orangutans 

Answer 1

If you let m= # of monkeys and r = # of orangutans (r is easier to use than o) you want to set up two equations in two unknowns:

 

 (number of monkeys) x (bananas eaten/monkey) + (number of orangutans) x (bananas eaten/orangutan)=111

 

1.      (m x 5) + (r x 8) = 111

 

but also  

 

2.         m+r =18            or     r = 18-m

 

then just plug (18-m) into 'r' in the first equation and solve for r. That should already give you the answer, but to be complete, use equation 2 to get m.

Answer 2

Let x = number of monkeys

       y = number of orangutans

 

Then, x + y = 18

          5x + 8y = 111

 

Multiply the first equation by -5:     -5x  - 5y = -90

                                                              5x + 8y = 111

 

Add the equations to get:  3y = 21

 

So, y = 7 and x = 11

 

The answer is (B).