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

Answer:

567

Step-by-step explanation:

Answer 2

Answer:

Each fudge cookie has 80 calories.

Each lemon cream has 65 calories.

Step-by-step 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.