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?
Answers
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 months is given by the formula;
where
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 months is given by the formula;
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;
We group like terms to get;
Therefore Chris and Kyle will have the same number of baseball cards after 11 months.
Final answer:
By setting equal the linear expressions for how many baseball cards Chris and Kyle have after a given number of months, we find that it will take 10 months for them to have the same number.
Explanation:
The question is essentially asking how long it will take for Chris and Kyle to have the same number of baseball cards. It's a problem about linear expressions, rooted in mathematics. Chris starts with 20 baseball cards and adds 3 per month. We can express this as C = 20 + 3m, where m is the number of months. Kyle starts with 40 baseball cards and adds 1 per month. We express this as K = 40 + m.
We want to find out when Chris and Kyle will have the same number of cards, so we set C = K, which results in 20 + 3m = 40 + m. By solving this equation, we can condense it to 2m = 20 or m = 10. Therefore, it will take 10 months for Chris and Kyle to have the same number of baseball cards.
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