Question

At a candy store, Brooke bought 1

pound of jelly beans and 6 pounds
of gummy worms for $42
Meanwhile, Ken bought 5 pounds
of jelly beans and 4 pounds of
gummy worms for $54. How
much does one pound of jelly
beans and one pound of gummy
worms candy cost?

Answer 1

One pound of jelly beans and one pound of gummy worms candy cost $6 each

Explanation:

Given

Let

`J \to` Jelly Beans

`G \to` Gummy worms

So, we have:

Brook

`J + 6G = 42`

Ken

`5J + 4G = 54`

Make J the subject in the first equation

`J + 6G = 42`

`J = 42 - 6G`

Substitute
`J = 42 - 6G` in
`5J + 4G = 54`

`5*[42 - 6G] + 4G = 54`

Open bracket

`210 - 30G + 4G = 54`

`210 -26G = 54`

Collect like terms

`-26G = 54 - 210\\`

`-26G = -156`

Divide both sides by -26

`G = 6`

Substitute
`G = 6` in
`J = 42 - 6G`

`J = 42 - 6*6`

`J = 42-36`

`J = 6`