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?
Well, it seems like Chris needs some catch-up lessons from Kyle's collection! Let's see how long it takes for them to reach the same level of baseball card greatness.
Chris is adding 3 cards per month, while Kyle is only adding 1 card per month. That means Chris is gaining on Kyle at a rate of 2 cards per month (3 - 1 = 2).
Since Kyle has a head start of 20 cards over Chris, we need to figure out how many 2-card months it will take for Chris to catch up.
20 divided by 2 equals 10. So, after 10 months, Chris will have added 30 cards (10 multiplied by 3 cards per month), bringing his total to 50 cards.
Meanwhile, Kyle has been truckin' along, adding just his usual 1 card per month. Therefore, after 10 months, he'll have added 10 cards (10 multiplied by 1 card per month), bringing his total to 50 cards as well.
Hurray! After 10 months, Chris and Kyle will finally have the same number of baseball cards! They'll be neck and neck in their race to become the reigning card collectors.
To find out after how many months Chris and Kyle will have the same number of baseball cards, we can set up an equation.
Let's assume it will take "x" months for Chris and Kyle's collections to have the same number of baseball cards.
After x months, Chris will have 20 + 3x baseball cards.
After x months, Kyle will have 40 + 1x baseball cards.
To solve for x, we set the number of baseball cards equal to each other:
20 + 3x = 40 + 1x
Subtracting 1x from both sides, we have:
2x = 20
Dividing both sides by 2, we get:
x = 10
Therefore, it will take 10 months for Chris and Kyle to have the same number of baseball cards.
To solve this problem, we need to determine the number of months it will take for Chris and Kyle to have the same number of baseball cards.
Let's start by finding the difference in the number of baseball cards between Chris and Kyle. Chris has 20 cards, and Kyle has 40 cards, so the difference is 40 - 20 = 20 cards.
Next, we need to determine the rate at which the number of cards increases for each person. Chris adds 3 cards per month, and Kyle adds 1 card per month.
To find the number of months it will take for Chris and Kyle to have the same number of cards, we can divide the initial difference of 20 cards by the rate of card accumulation.
20 cards / (3 cards per month - 1 card per month) = 20 cards / 2 cards per month = 10 months
Therefore, it will take Chris and Kyle 10 months to have the same number of baseball cards.
Chris: 20 + 3n
Kyle : 40 + n
they are equal when
20+3n = 40+n
solve for n