You visit an animal rescue in australia that serves primarily kangaroos and dingoes. you ask the zookeeper how many of each animal they have, and she decided to test your reasoning ability. she tells you that when she feeds the animals she counts a total of 116 feet where kangaroos have two feet and dingoes have 4 feet. she can also count a total of 34 heads. how many kangaroos and dingoes are at this animal rescue?

There are 10 kangaroos and 24 dingoes in this animal rescue.

Step-by-step explanation:

Given,

Total head count = 34 heads

∴ Kangaroos + Dingoes = 34

Let us assume,

Number of kangaroos as "x" and number of dingoes as "y"

The equation can be framed as x + y = 34

The number of feet for kangaroo = 2 feet

The number of feet for dingoes = 4 feet

The total number of feet = 116 feet

So, the equation can be framed as 2x + 4y = 116

Step 1 : Muliply the 1st equation by 2.

The new equation is 2x + 2y = 68

step 2 : Subtract the above equation with the second equation.

    2x + 2y = 68

  -2x - 4y = -116

          -2y = -48

step 3 : Therefore, y =24. Substitute y=24 in the 1st equation.

x + 24 = 34

x = 34-24

x = 10

Kangaroos, x = 10 kangaroos

Dingoes, y = 24 dingoes

a negative exponent is translated as follows:

so, we have