Question

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.

Answer 1

The solution to this system of equations is:

• B = 28
• T = 19

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.

`\text{tarantulas + butterflies} = 47`

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

`T + B = 47`

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:

`6B + 8T = 320`

Now, we can set up a system of equation.

`\displaystyle \left \{ {{B + T = 47} \atop {6B + 8T = 320}} \right.`

Using the first equation, we can solve for B.

`\displaystyle B + T = 47\\\\B + T - T = 47 - T\\\\B = 47 - T`

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

`\displaystyle 6(47-T)+8T=320\\\\282 - 6T + 8T = 320\\\\282 + 2T = 320\\\\2T + 282 = 320\\\\2T + 282 - 282 = 320 -282\\\\2T = 38\\\\(2T)/(2)=(38)/(2)\\\\T = 19`

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

`B + 19 = 47\\\\B + 19 - 19 = 47 - 19\\\\B = 28`

Therefore, the solution to this system of equations is:

• B = 28
• T = 19