Jill has a collection of bugs. Her collection contains butterflies and tarantulas. She has 47 bugs and counts 320 total legs. (Note: butterflies have 6 legs and tarantulas have 8 legs) If T represents the number of tarantulas and B represents the number of butterflies, complete the below system of equations.

The solution to this system of equations is:

Step-by-step explanation:

We are given that Jill has 47 bugs and counts a total 320 legs.

We can concur that by adding the total number of butterflies and the total number of tarantulas, we will get 47 bugs.

We are also told that T is tarantulas and B is butterflies.

Then, we also know that butterflies have 6 legs and tarantulas have 8 legs. So, for every tarantula, we get a multiple of 8 and for butterflies, we get a multiple of 6. This gives us a new equation:

Now, we can set up a system of equation.

Using the first equation, we can solve for B.

Then, we can substitute this value of B into the second equation and solve for T.

Finally, we can substitute this value of T into the first equation to solve for B.

Therefore, the solution to this system of equations is:

1,645,493,059.35

step-by-step explanation: