Both David and Eric had an equal amount of money at first. Every month, David spent $850 and Eric spent $912. After a few months, David was left with $1550 while Eric had 4/5 of the money David had left. How much did Eric have at first?
4/5 of $1550 = $1240
If they both started with $x and spent for m months, then
x - 912m = 1240
x - 850m = 1550
Subtract to find that they spent money for 5 months
so Eric started with 1240 + 5*912 = $5800
amount of money each had at first --- x
after n months:
David had x - 850n
Eric had x - 912n
x - 850n = 1550
x = 1550 + 850n , #1
x - 912n = (4/5)1550 , #2
5x - 4560n = 6200
5x = 6200 + 4560n
x = 1240 + 912n
912n + 1240 = 1550 + 850n
62n = 310
n = 5
then x = 1240 + 912(5) = 5800
Since it said that they had equal amounts , Eric had 5800
To find out how much money Eric had at first, let's break down the information we have step by step:
1. Initially, David and Eric had an equal amount of money. Let's say they both had "x" dollars.
2. Every month, David spent $850. So, after a certain number of months, David was left with $1550.
3. This means that David's original amount of money minus what he spent ($850 multiplied by the number of months) equals $1550. Mathematically, we can write this as:
x - 850m = 1550, where "m" represents the number of months it took.
4. We're also told that Eric had 4/5 of the money David had left. We can express this information as:
Eric's amount of money = (4/5) * David's amount of money = (4/5) * (x - 850m).
5. Now, we have two equations:
x - 850m = 1550 (Equation 1)
Eric's amount of money = (4/5) * (x - 850m) (Equation 2)
Our goal is to find the value of "x", which represents Eric's initial amount of money.
6. Let's solve this system of equations. We can substitute Equation 2 into Equation 1:
x - 850m = 1550
(4/5) * (x - 850m) = (4/5) * (1550)
Simplifying these equations yields:
x - 850m = 1550
4x - 3400m = 3100
7. Let's multiply both sides of the first equation by 4 to eliminate the decimals:
4(x - 850m) = 4 * 1550
4x - 3400m = 3100
This simplifies to:
4x - 3400m = 6200
4x - 3400m = 3100
8. Subtract the second equation from the first:
(4x - 3400m) - (4x - 3400m) = 6200 - 3100
This results in:
0 = 3100
9. This means that the equations are contradictory, and there is no solution. However, this contradicts the initial assumption that both David and Eric had an equal amount of money. Therefore, there is no valid solution to this problem.
Based on the given information, it's not possible to determine Eric's initial amount of money.