Adam, Billy and Chandra each gave the same amount of money to Don who had no money. Adam gave Don 1/4 of his money Billy gave Don 2/7 of his money. Chandra gave Don 1/3 of his money.
(a) What fraction of the total sum of money the 3 boys had did Don
receive?
(b) Don had $96 in the end. How much did Adam have at first?
To solve this problem, we can start by finding the common denominator for the fractions 1/4, 2/7, and 1/3. The common denominator is 84.
(a) Adam gave Don 1/4 of his money, which is (1/4) * 84 = 21 units of money.
Billy gave Don 2/7 of his money, which is (2/7) * 84 = 24 units of money.
Chandra gave Don 1/3 of his money, which is (1/3) * 84 = 28 units of money.
The total amount of money the three boys gave is 21 + 24 + 28 = 73 units of money.
Don received 73 units of money out of the total of 84 units of money. So the fraction of the total sum of money the three boys had that Don received is 73/84.
(b) If Don had $96 in the end, then 73 units of money is equal to $96.
So 1 unit of money is equal to $96/73.
Adam gave Don 21 units of money, so Adam had 21 * ($96/73) = $27.84 at first. Answer: \boxed{27.84}.
To find out the answer, we need to first determine the fraction of the total sum of money each boy gave to Don.
(a) Let's calculate the fractions for each boy:
- Adam gave 1/4 of his money.
- Billy gave 2/7 of his money.
- Chandra gave 1/3 of his money.
To find the total fraction of the money Don received, we need to add up these fractions.
1/4 + 2/7 + 1/3 = (21/84) + (48/84) + (28/84)
= 97/84
Therefore, Don received (97/84) of the total sum of money.
(b) Since we know that Don had $96 in the end, we can set up an equation to solve for Adam's original amount of money.
Let's assume Adam had x dollars at first. According to the problem, 1/4 of Adam's money is equal to $96:
(1/4) * x = 96
To solve for x, we can multiply both sides of the equation by 4:
x = 96 * 4
x = 384
So, Adam had $384 at first.