Ann bob and cindy had some money. Ann had 20% of the total of the three kids.Bob's amount is 50% of the total amount of ann's and cindys. if cindy has $48 more than bob, how much money does cindy have?
a = .2 (a + b + c)
4a = b + c
b = .5 (a + c) ... 2b = a + c
... a = 2b - c ... b + c = 8b - 4c
... 5c = 7b ... 5b + 240 = 7b
... b = 120
c = b + 48 = 168
Let's assume the total amount of money the three kids have is 100%.
Since Ann has 20% of the total amount, this means Ann has 20/100 * Total amount = 0.20 * Total amount.
Bob's amount is 50% of the total amount of Ann's and Cindy's money, which means Bob has 50/100 * (Ann's amount + Cindy's amount) = 0.50 * (0.20 * Total amount + Cindy's amount).
We are also given that Cindy has $48 more than Bob, so we can write this as Cindy's amount - Bob's amount = $48.
Combining the equations, we have:
Cindy's amount - 0.50 * (0.20 * Total amount + Cindy's amount) = $48.
Simplifying the equation, we have:
Cindy's amount - 0.10 * Total amount - 0.50 * Cindy's amount = $48.
Multiplying and rearranging terms, we have:
0.50 * Cindy's amount - 0.10 * Total amount = $48.
Now, let's substitute the value of Cindy's amount from the given information, which is Ann's amount + $48:
0.50 * (Ann's amount + $48) - 0.10 * Total amount = $48.
Expanding and simplifying, we get:
0.50 * Ann's amount + 0.50 * $48 - 0.10 * Total amount = $48.
0.50 * Ann's amount - 0.10 * Total amount = $48 - 0.50 * $48.
0.50 * Ann's amount - 0.10 * Total amount = $48 - $24.
0.50 * Ann's amount - 0.10 * Total amount = $24.
Now, let's substitute the value of Ann's amount from the given information, which is 0.20 * Total amount:
0.50 * (0.20 * Total amount) - 0.10 * Total amount = $24.
Expanding and simplifying, we get:
0.10 * Total amount - 0.10 * Total amount = $24.
0 = $24.
The equation is not possible to solve because it leads to an invalid conclusion. Please check if any information is missing or incorrect.
To solve this problem, we need to break it down step by step.
Let's say the total amount of money that Ann, Bob, and Cindy have combined is x dollars.
According to the information given, Ann has 20% of the total amount. Therefore, Ann has 0.2x dollars.
Bob's amount is 50% of the total of Ann's and Cindy's amounts. Since Cindy has $48 more than Bob, we can represent Bob's amount as y dollars, and Cindy's amount as y + $48.
So, Bob's amount (y) is 50% of Ann's amount (0.2x) and Cindy's amount (y + $48), which can be written as:
y = 0.5 * (0.2x + y + $48)
Let's solve this equation to find the value of y:
First, distribute the 0.5 to the terms inside the parentheses:
y = 0.1x + 0.5y + 0.5($48)
Simplify further:
y - 0.5y = 0.1x + 0.5($48)
0.5y = 0.1x + $24
Subtract 0.1x from both sides:
0.5y - 0.1x = $24
Multiply both sides by 10 to remove the decimal:
5y - x = $240
Now, we can use the information that Cindy has $48 more than Bob, which can be written as:
y + $48 = Cindy's amount
We can substitute this expression for y in the equation we obtained earlier:
5(y + $48) - x = $240
Let's simplify this equation further:
5y + 5($48) - x = $240
5y + $240 - x = $240
Subtract $240 from both sides:
5y - x = $0
Since 5y - x = $0 and we already know that 5y - x = $240, we can equate these two expressions:
$0 = $240
This equation is not possible to solve because it does not make sense. Therefore, the problem may have been set up incorrectly, or there might be an error in the given information.