Ethan has $120 more than Dilton. After Ethan spent 80% of his money and Dilton spent 60% of his money, they still have $270 left altogether. How much money does Ethan have left in the end?
Dilton's amount --- x
Ethan's amount ---- x+120
amount left after the spending spree:
Ethan: 0.2(x+120)
Dilton: .4x
.4x + .2(x+120) = 270
.4x + .2x + 24 = 270
calculate the rest and state you conclusion
E = Ethan's money in beginning
D = Dilton's money in beginning
Ethan has $120 more than Dilton means:
E = D + 120
After Ethan spent 80% of the money he got 20% of the money.
20% = 20/100 = 0.2
Ethan has 0.2 ( D + 120 ) money left
After Dilton spent 60% of the money, he got 40% of the money.
40% = 40 / 100 = 0.4
Dilton has 0.4 D of money left.
In total they have left:
0.2 ( D + 120 ) + 0.4 D = 270
0.2 D + 24 + 0.4 D = 270
0.6 D + 24 = 270
Subtract 24 to moth sides
0.6 D = 246
D = 246 / 0.6 = 410
Dilton have $410 in beginning
E = D + 120
E = $410 + $120 = $530 in beginning
After Ethan spent 80% of the money he got 20% of the money.
20% = 20 / 100 = 0.2
In the end Ethan have left 0.2 ∙ $530 = $106
To solve this problem, we can break it down into steps:
Step 1: Assign variables
Let's assign variables to represent the amount of money Ethan and Dilton initially have.
Let "E" be the amount of money Ethan has initially
Let "D" be the amount of money Dilton has initially
Step 2: Set up equations
From the given information, we know that Ethan has $120 more than Dilton. Therefore we can write the equation:
E = D + $120
Step 3: Determine the amount they each spent
Ethan spent 80% of his money, so the amount he has left is 100% - 80% = 20% of his initial money.
Dilton spent 60% of his money, so the amount he has left is 100% - 60% = 40% of his initial money.
Step 4: Convert percentages to decimals
To calculate the amount they each have left, we need to convert the percentages to decimals.
Ethan has 20% of his initial money left, which is 20/100 = 0.2.
Dilton has 40% of his initial money left, which is 40/100 = 0.4.
Step 5: Set up equations for the remaining money
We know that the amount they have left altogether is $270.
Therefore, we can set up the following equation:
0.2E + 0.4D = $270
Step 6: Solve the system of equations
Now we have two equations:
E = D + $120
0.2E + 0.4D = $270
We can solve this system of equations to find the values of E and D.
Using the first equation, we can substitute E with D + $120 in the second equation:
0.2(D + $120) + 0.4D = $270
Simplifying the equation:
0.2D + $24 + 0.4D = $270
0.6D + $24 = $270
Subtract $24 from both sides:
0.6D = $270 - $24
0.6D = $246
Divide both sides by 0.6:
D = $246 / 0.6
D ≈ $410
Step 7: Find the remaining money Ethan has
Using the first equation, we can substitute D with $410:
E = $410 + $120
E = $530
Therefore, Ethan has $530 left in the end.