David and robort have 120 baseball cards.David gives robort one third of his cards and then 10 more cards.Robort now has five times as many cards David.How many cards robort have originally
David gave Robert D/3 + 10
now David has D - D/3 - 10
Robert has R + D/3 + 10
so
R + D/3 + 10 = 5 (D - D/3 -10)
3 R + D + 30 = 15 D - 5 D - 150
3 R - 9 D = - 180
R - 3 D = - 60
but we know R+D = 120
so
R + D =120
R - 3 D = -60
-----------------subtract
4 D = 180
D = 45
R = 120 - 45 = 75
Let's break down the information step by step:
1. David and Robort have 120 baseball cards in total.
2. David gives Robort one-third of his cards. This means David gives Robort (1/3) * 120 = <<(1/3)*120=40>>40 cards.
3. After receiving 40 cards from David, Robort now has (40 + 10) = <<40+10=50>>50 cards.
4. The problem states that Robort now has five times as many cards as David. Therefore, David originally had 50 / 5 = <<50/5=10>>10 cards.
So, Robort originally had 10 cards.
To find out the original number of cards Robort had, we can work backwards from the information given.
Let's assume that the original number of cards Robort had was x.
According to the given information, David gave Robort one-third of his cards plus 10 cards. Therefore, David gave (1/3)x + 10 cards to Robort.
After receiving the cards from David, Robort had five times as many cards as David. So, the equation becomes:
(1/3)x + 10 = 5(120 - (1/3)x)
Now, we can solve this equation to find the value of x, which represents the original number of cards Robort had.
First, distribute 5 to both terms in the parentheses:
(1/3)x + 10 = 600 - (5/3)x
Next, bring all terms involving x to one side:
(1/3)x + (5/3)x = 600 - 10
Combine like terms:
(6/3)x = 590
Simplify:
2x = 590
Divide both sides by 2:
x = 295
Therefore, the original number of cards Robort had was 295 cards.
Well, from the information given, we can gather that after David gives one third of his cards and then 10 more cards, Robort ends up with five times as many cards as David. So, let's try to figure this out with some clown math!
Let's say David originally had "D" cards, and Robort originally had "R" cards.
According to the given information, David gives (1/3)D + 10 cards to Robort. So now Robort has (1/3)D + 10 cards, and David has D - [(1/3)D + 10] cards.
It's also given that Robort now has five times as many cards as David:
(1/3)D + 10 = 5(D - [(1/3)D + 10])
Now, let's solve this equation to find out the original number of cards Robort had. Hang on to your clown noses!
(1/3)D + 10 = 5D - (5/3)D - 50
(1/3)D + (5/3)D = 5D - 5D - 50 - 10
(6/3)D = -60
2D = -60
D = -30
Uh-oh, it seems we've encountered some clown logic. It seems that David originally had a negative number of cards, which doesn't make sense. So, there might be a mistake in the information or calculations. Let's give it another try, shall we?
David has x cards.
x-x/3-10 = 2x/3-10 left.
2x/3-10 + 5(2x/3-10) = 120
2x/3-10(1+5) = 120
2x/3-10 = 20
2x/3 = 30
X = 45 cards.
Robert had120-45 = 75 cards, originally.