Jules and Nathan share a sum of money. Jules receives 7/10 of the amount. after jules gives nathan $26 they both have the same amount of money. find the amount of the sum that the two boys shared
Let's assume that the sum of money that Jules and Nathan shared is represented by the variable "x".
According to the given information, Jules received 7/10 of the amount, which is (7/10)*x = 7x/10.
After Jules gives Nathan $26, Jules will have (7x/10) - 26.
On the other hand, Nathan will receive $26 from Jules and his new total will be x/10 + 26.
Since they both have the same amount of money, we can set up an equation:
(7x/10) - 26 = x/10 + 26
Multiplying both sides of the equation by 10 to eliminate the denominators, we get:
7x - 260 = x + 260
Subtracting x from both sides of the equation, we get:
6x - 260 = 260
Adding 260 to both sides of the equation, we get:
6x = 520
Dividing both sides of the equation by 6, we get:
x = 520/6
Simplifying the fraction, we get:
x = 86.67
Therefore, the sum of money that the two boys shared is approximately $86.67.
130
Let's assume that the sum of money that Jules and Nathan shared is represented by the variable "x".
According to the given information, Jules received 7/10 of the amount, which is (7/10)*x = 7x/10.
After Jules gives Nathan $26, Jules will have (7x/10) - 26.
On the other hand, Nathan will receive $26 from Jules and his new total will be x/10 + 26.
Since they both have the same amount of money, we can set up an equation:
(7x/10) - 26 = x/10 + 26
Multiplying both sides of the equation by 10 to eliminate the denominators, we get:
7x - 260 = x + 260
Subtracting x from both sides of the equation, we get:
6x - 260 = 260
Adding 260 to both sides of the equation, we get:
6x = 520
Dividing both sides of the equation by 6, we get:
x = 520/6
Simplifying the fraction, we get:
x = 86.67
Therefore, the sum of money that the two boys shared is $86.67.
To solve this problem, we can use algebraic equations to represent the given information and then solve for the total amount of money that Jules and Nathan shared.
Let’s denote:
The total amount of money as T
The amount of money Jules received as 7/10T
The amount of money Nathan received as 3/10T
We are given that after Jules gives $26 to Nathan, they both have the same amount of money. This can be represented by the equation:
(7/10)T - 26 = (3/10)T + 26
Solving this equation will give us the total amount of money they shared.
Solution
First, let’s simplify the equation:
(7/10)T - (3/10)T = 26 + 26
This simplifies to:
(4/10)T = 52
Now, let’s solve for T:
(4/10)T = 52
Multiplying both sides by 10:
4T = 520
Dividing both sides by 4:
T = 130
So, the total amount of money that Jules and Nathan shared is $130.