Question

Two lemon creams plus four fudge cookies have 450 calories. Four lemon creams plus two fudge cookies have 420 calories. How many calories are in each cookie?

Answer 1

567

Explanation:

Answer 2

Each fudge cookie has 80 calories.

Each lemon cream has 65 calories.

Explanation:

We will let
`\ell` represent the calories in lemon creams and
`f` represent the calories in fudge cookies.

Two lemon creams and four fudge cookies together have 450 calories. So, we can write the following equation:

`2\ell+4f=450`

And four lemon creams plus two fudge cookies together have 420 calories. So, we can write the following equation:

`4\ell+2f=420`

We now have a system of equations. We can solve this by elimination.

For the first equation, we can multiply both sides by -2. This way, the
`\ell` will cancel when we add the two equations together.

So, the first equation becomes:

`-4\ell-8f=-900`

Add this to the second equation. Hence:

`(-4\ell+4\ell)+(-8f+2f)=(-900+420)`

Simplify:

`-6f=-480`

Divide both sides by -6. Hence:

`f=80`

So, there are 80 calories in one cookie.

We can use the first equation again to find the amount of calories in one cream. We have:

`2\ell+4f=450`

Substituting 80 for
`f` yields:

`2\ell+320=450`

Then it follows that:

`\ell=65`

So, there are 65 calories in each lemon cream.