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?

Each fudge cookie has 80 calories.

Each lemon cream has 65 calories.

Step-by-step explanation:

We will let represent the calories in lemon creams and represent the calories in fudge cookies.

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

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

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 will cancel when we add the two equations together.

So, the first equation becomes:

Add this to the second equation. Hence:

Simplify:

Divide both sides by -6. Hence:

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:

Substituting 80 for yields:

Then it follows that:

So, there are 65 calories in each lemon cream.

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