Sammy has $15 more than Billy .mary has twice as much as Sammy. James has$5 less than Mary. Together they have $130.how much does each person have?
B = Bill's money
S = Sammy's money
M = Mary's money
J = James's money
Sammy has 15 $ more than Billy.
S = B + 15
Mary has twice as much as Sammy.
M = 2 S = 2 ( B + 15 ) = 2 B + 2 * 15 = 2 B + 30
James has 5 $ less than Mary.
J = M - 5 = 2 B + 30 - 5 = 2 B + 25
Together they have 130 $
B + S + M + J = 130
Enter values B, M, J and S in this expression.
B + B + 15 + 2 B + 30 + 2 B + 25 = 130
6 B + 70 = 130 Subtract 70 to both sides
6 B + 70 - 70 = 130 - 70
6 B = 60 Divide both sides by 6
B = 60 / 6 = 10 $
S = B + 15 = 10 + 25 = 25 $
M = 2 B + 30 = 2 * 10 + 30 = 20 + 30 = 50 $
J = 2 B + 25 = 2 * 10 + 25 = 20 + 25 = 45 $
To solve this problem, let's assign variables to represent each person's amount of money.
Let's say:
Billy has x dollars.
Sammy has x + 15 dollars.
Mary has 2(x + 15) dollars.
James has 2(x + 15) - 5 dollars.
Now, we can set up an equation based on the given information:
x + (x + 15) + 2(x + 15) + (2(x + 15) - 5) = 130
Let's solve it step by step:
Combine like terms:
x + x + 15 + 2x + 30 + 2x + 30 - 5 = 130
6x + 65 = 130
Subtract 65 from both sides:
6x = 65
Divide both sides by 6:
x = 10.83 (approximately)
Now, we know that Billy has $10.83. We can substitute this value back into our equations to find out how much money the others have.
Sammy's amount:
x + 15
10.83 + 15 = $25.83
Mary's amount:
2(x + 15)
2(10.83 + 15) = $52.66
James's amount:
2(x + 15) - 5
2(10.83 + 15) - 5 = $47.66
So, the final answer is:
Billy has $10.83, Sammy has $25.83, Mary has $52.66, and James has $47.66.