Gary and Jacky had $825 altogether.
Gary spent 4/5 of his money and Jacky spent 3/5 of his. Then they found that they each had an equal amount of money left. How much did each of them have left?
Each of them had $175 left.
To solve this problem, we need to find out how much money each person initially had and then calculate how much money they each had left.
Let's assume Gary had x amount of money, and Jacky had y amount of money.
According to the given information, Gary spent 4/5 of his money. So, he had 1 - 4/5 = 1/5 of his money left.
Similarly, Jacky spent 3/5 of his money. Therefore, he had 1 - 3/5 = 2/5 of his money left.
We know that Gary and Jacky had $825 altogether, so we can set up an equation: x + y = 825.
Now, let's calculate how much money each person had left.
Gary had 1/5 of his money left, which means he had 1/5 * x.
Jacky had 2/5 of his money left, which means he had 2/5 * y.
Since they both had an equal amount of money left, we can set up another equation: 1/5 * x = 2/5 * y.
Now, we can solve this system of equations to find the values of x and y.
From the first equation, we can isolate x: x = 825 - y.
Substituting this into the second equation: 1/5 * (825 - y) = 2/5 * y.
To simplify, we can multiply both sides by 5: 825 - y = 2y.
Combining like terms: 825 = 2y + y.
Simplifying further: 825 = 3y.
Dividing both sides by 3: y = 275.
Substituting y = 275 back into x = 825 - y: x = 825 - 275 = 550.
So, Gary had $550 and Jacky had $275 initially.
To find out how much money they had left, we can substitute these values into the equations.
Gary had 1/5 of his money left: 1/5 * 550 = $110.
Jacky had 2/5 of his money left: 2/5 * 275 = $110.
Therefore, Gary and Jacky each had $110 left.
Let's start by finding how much money Gary and Jacky had initially.
Let's say Gary had x dollars.
And Jacky had y dollars.
According to the first information given, the total amount of money they had together is $825.
So, we can write the equation: x + y = 825 .......(equation 1)
According to the second information given, Gary spent 4/5 of his money, which means he has 1/5 of his money left.
So, the amount of money Gary has left is x/5.
Similarly, Jacky spent 3/5 of his money, which means he has 2/5 of his money left.
So, the amount of money Jacky has left is 2y/5.
According to the third information given, they found that they each had an equal amount of money left.
So, we can write the equation: x/5 = 2y/5 .......(equation 2)
To solve these equations, we can substitute the value of x from equation 1 into equation 2.
Substituting x = 825 - y into equation 2, we get:
(825 - y)/5 = 2y/5
Cross-multiplying, we get:
5(825 - y) = 2y
Expanding, we get:
4125 - 5y = 2y
Bringing the y terms to one side, we get:
7y = 4125
Dividing both sides by 7, we get:
y = 4125/7 = 589.29
Since we cannot have a fraction of a dollar as the amount of money, we round it to the nearest whole dollar.
So, Jacky initially had $589.
Now, substituting this value of y into equation 1 to find x:
x + 589 = 825
x = 825 - 589 = 236
Therefore, Gary initially had $236.
Now, to find out how much money they each have left, we can substitute these values into their respective equations:
Amount of money Gary has left = x/5 = 236/5 = $47.20
Amount of money Jacky has left = 2y/5 = 2(589)/5 = $235.60