Jenny,Bob and Paul share a sum of money. Jenny received 2/5 of the money, Bob received 1/4 of the money and Paul received the rest of the money. If Paul received $1.50 more than Bob, how much more money did Jenny receive than Paul.
please show your work
To find out how much more money Jenny received than Paul, we need to calculate the amount received by each person. We can break down the given information step-by-step.
1. Let's assume the total amount of money shared by Jenny, Bob, and Paul is represented by 'x'.
2. According to the problem, Jenny received 2/5 of the money. So, Jenny's share is (2/5) * x.
3. Bob received 1/4 of the money. Hence, Bob's share is (1/4) * x.
4. Paul received the rest of the money, which implies that Paul's share is the remaining amount after giving Jenny and Bob their shares. Therefore, Paul's share is x - [(2/5) * x + (1/4) * x].
5. It is given that Paul received $1.50 more than Bob. So, we can write the equation: Paul's share = Bob's share + $1.50.
Now, let's put this information together and solve the problem.
Paul's share = Bob's share + $1.50
[x - ((2/5) * x + (1/4) * x)] = [(1/4) * x] + $1.50
Simplify the equation:
[(20/20) * x - (8/20) * x - (5/20) * x] = [(5/20) * x] + $1.50
[(7/20) * x] = [(5/20) * x] + $1.50
To solve for 'x', we can multiply both sides of the equation by 20 to eliminate the denominators:
7x = 5x + 30
Now, simplify the equation further:
7x - 5x = 30
2x = 30
x = 15
Therefore, the total amount of money shared among Jenny, Bob, and Paul is $15.
Now, we can calculate the amounts received by Jenny, Bob, and Paul.
Jenny's share = (2/5) * x = (2/5) * 15 = $6
Bob's share = (1/4) * x = (1/4) * 15 = $3.75
Paul's share = x - [(2/5) * x + (1/4) * x] = 15 - (6 + 3.75) = $5.25
To find out how much more money Jenny received than Paul, we subtract Paul's share from Jenny's share.
Difference = Jenny's share - Paul's share = $6 - $5.25 = $0.75
Therefore, Jenny received $0.75 more than Paul.