Question

Chris has a collection of 20 baseball cards and Kyle has collection of 40 baseball cards. Chris is adding 3 baseball cards per month to his collection while Kyle is adding one baseball card per month to his collection. After how many months will Chris and Kyle have the same number of baseball cards?

Answer 1

Answer:

11 months

Step-by-step explanation:

The initial number of baseball cards that Chris has is 20.

This is like the first term of a sequence.

If Chris is adding 3 baseball cards per month, then there will be a constant difference of 3.

The number of baseball cards after $n$ months is given by the formula;

$C_n=20+(n-1)3$

$\Rightarrow C_n=20+3n-3$

$\Rightarrow C_n=3n+17$ where $n\ge1$

Similarly, Kyle initially has 40 baseball cards and adds one base ball card per month to  his collection;

The number of his baseball cards after $n$ months is given by the formula;

$K_n=40+(n-1)1$

$K_n=40+n-1$

$\Rightarrow K_n=n+39$

To determine the number of months that will pass before Kyle and Chris have the same number of base ball cards, we equate both equations to get;

$\Rightarrow 3n+17=n+39$

We group like terms to get;

$3n-n=39-17$

$\Rightarrow 2n=22$

$\Rightarrow n=11$

Therefore Chris and Kyle will have the same number of baseball cards after 11 months.