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 [tex]n[/tex] months is given by the formula;
[tex]C_n=20+(n-1)3[/tex]
[tex]\Rightarrow C_n=20+3n-3[/tex]
[tex]\Rightarrow C_n=3n+17[/tex] where [tex]n\ge1[/tex]
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 [tex]n[/tex] months is given by the formula;
[tex]K_n=40+(n-1)1[/tex]
[tex]K_n=40+n-1[/tex]
[tex]\Rightarrow K_n=n+39[/tex]
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;
[tex]\Rightarrow 3n+17=n+39[/tex]
We group like terms to get;
[tex]3n-n=39-17[/tex]
[tex]\Rightarrow 2n=22[/tex]
[tex]\Rightarrow n=11[/tex]
Therefore Chris and Kyle will have the same number of baseball cards after 11 months.
