Question

Marion bought 14 packages of plastic frog and lizard fishing lures. She bought frog lures in packages of 4 and lizard lures in packages of 6 for a total of 72 lures. How many of each lure did Marion buy?

Answer 1

Marion bought 6 frog lures and 8 lizard fishing lures.

Explanation:

Let
`f` represent frog lures and
`l` represent lizard lures.

The total packages Marion bought is

`f+l=14...eqn1`

If she bought frog lures in packages of 4 and lizard lures in packages of 6 for a total of 72 lures, then

`4f+6l=72...eqn2`

We make
`f` the subject in equation 1 and put it into equation 2 to get;

`f=14-l...eqn3`

We put equation 3 into equation 2 to get;

`4(14-l)+6l=72`

`\Righttarrow 2(14-l)+3l=36`

We expand the bracket to get;

`28-2l+3l=36`

`-2l+3l=36-28`

`l=8`

We put
`l=8` into equation 3 to get;

`f=14-8`

`f=6`

Therefore Marion bought 6 frog lures and 8 lizard fishing lures.