Aaron and Benga have a total of 976 trading cards. Benga has 7 times as many cards as Aaron. How many cards should Benga give Aaron so that Aaron will have 3 times as many cards as Benga?
tanku
Let's start by setting up equations based on the given information:
Let's assume that Aaron has x trading cards.
According to the problem, Benga has 7 times as many cards as Aaron, which means Benga has 7x trading cards.
We also know that the total number of trading cards they have is 976, so we can create an equation from this information:
x + 7x = 976
Simplifying the equation gives us:
8x = 976
To find the value of x, we need to divide both sides of the equation by 8:
x = 976/8
x = 122
So, Aaron has 122 cards and Benga has 7 times as many, which is 7*122 = 854 cards.
Now, let's find out how many cards Benga needs to give to Aaron so that Aaron will have 3 times as many cards as Benga.
Let's assume that Benga gives y cards to Aaron.
After giving y cards to Aaron, Aaron will have x + y cards.
Benga will have 854 - y cards left.
According to the problem, Aaron will have 3 times as many cards as Benga:
x + y = 3(854 - y)
Simplifying the equation gives us:
x + y = 2562 - 3y
Rearranging the equation gives us:
x + 4y = 2562
Substituting the value of x from the previous equation gives us:
122 + 4y = 2562
To isolate y, we subtract 122 from both sides of the equation:
4y = 2562 - 122
4y = 2440
Dividing both sides of the equation by 4 gives us:
y = 2440/4
y = 610
Therefore, Benga should give 610 cards to Aaron so that Aaron will have 3 times as many cards as Benga.
To solve this problem, we can use algebraic equations.
Let's assume that Aaron has x trading cards. Since Benga has 7 times as many cards as Aaron, Benga will have 7x trading cards.
According to the problem, the total number of trading cards they have is 976. So we can set up the equation:
x + 7x = 976
Combining like terms, we get:
8x = 976
Solving for x, we divide both sides of the equation by 8:
x = 976/8
x = 122
Now we know that Aaron has 122 trading cards. To find out how many cards Benga has, we can substitute this value into 7x:
7x = 7 * 122
7x = 854
Therefore, Benga has 854 trading cards.
To figure out how many cards Benga should give Aaron so that Aaron will have 3 times as many cards as Benga, we can set up an equation:
x + cards_given = 3 * (854 - cards_given)
Simplifying the equation:
x + cards_given = 3 * 854 - 3 * cards_given
x + cards_given = 2562 - 3 * cards_given
Adding 3 * cards_given to both sides:
4 * cards_given = 2562 - x
Substituting the known values:
4 * cards_given = 2562 - 122
4 * cards_given = 2440
Dividing both sides by 4:
cards_given = 2440 / 4
cards_given = 610
Therefore, Benga should give Aaron 610 trading cards so that Aaron will have 3 times as many cards as Benga.
Let A = number of Aaron's cards
Let B = number of Benga's cards
From the first statement, the total number of their cards is 976, so
A + B = 976
From the second statement,
B = 7A
Thus we can say,
A + 7A = 976
8A = 976
A = 122
B = 854
Now, let x = number of cards that Benga will give to Aaron.
According to the last condition,
122 + x = 3(854 - x)
Solving,
122 + x = 2562 - 3x
4x = 2440
x = 610 cards
Hope this helps :3