Aaron and Ben have a total of 976 trading cards. Ben has 7 times as many cards as Aaron. How many cards should Ben give Aaron so that Aaron will have 3 times as many cards as Ben?
right now:
x + 7x = 976
x= 122
Aaron has 122 cards and Ben has 854.
after the give-away of k cards:
ben has 854-k
Aaron has 122+k
Aaron has 3 times as many as Ben
122+k = 3(854 - k)
122+k = 2562 - 3k
4k = 2440
k = 610
check:
after the exchange
Ben has 854-610 = 244
Aaron has 122 + 610 = 732
which is 3(244)
To solve this problem, we can set up a system of equations based on the given information.
Let's assume Aaron has x trading cards.
According to the problem, Ben has 7 times as many cards as Aaron, so Ben has 7x trading cards.
We also know that the total number of trading cards is 976, so we can write the equation:
x + 7x = 976
Combining like terms:
8x = 976
We can solve for x by dividing both sides of the equation by 8:
x = 976 / 8
x = 122
Now that we know Aaron has 122 trading cards, we can calculate how many cards Ben has:
Ben = 7x = 7 * 122 = 854
To find out how many cards Ben should give Aaron so that Aaron will have 3 times as many cards as Ben, we can set up another equation:
3 * Ben = Aaron + x
Plugging in the values we know:
3 * 854 = 122 + x
Simplifying:
2562 = 122 + x
Rearranging the equation:
x = 2562 - 122
x = 2440
So Ben should give Aaron 2440 cards for Aaron to have 3 times as many cards as Ben.