# Rachel and Kyle both collect geodes. Rachel has 3 less than twice the number of geodes Kyle has. Kyle has 6 fewer geodes than Rachel.How do you write a system of equations to represent this situation and solve?

##### 1 Answer

Problems like this are solved using a system of equations. To create this system, look at each sentence and try to reflect it in the equation.

Assume, Rachel has

Let's transform into an equation the first statement about these quantities: "Rachel has 3 less than twice the number of geodes Kyle has." What it says is that

The next statement is "Kyle has 6 fewer geodes than Rachel." So,

So , we have a system of equations:

The easiest way to solve this system is to substitute

Open the parenthesis:

Add

So, the

The value of

So, Rachel has 15 geodes, Kyle has 9 geodes.

Checking step is very much desirable.

(a) Check "Rachel has 3 less than twice the number of geodes Kyle has."

Indeed, twice as Kyle has is

Rachel's 15 geodes are 3 less than 18.

(b) Check "Kyle has 6 fewer geodes than Rachel".

Indeed, Kyle's 9 geodes are 6 less than Rachel's 16.

This confirms the correctness of the obtained solution.