Barry had 60% of the amount Tom had. Tom had 2/3 more than Eddie. Given that the three men had $4400 altogether, how much did Tom have?
Eddie --- x
Tom ---- 5/3 x
Barry ---- (3/5)(5x/3) = x
x + 5x/3 + x = 4400
3x + 5x + 3x = 13200
x = 1200
So Eddie has 1200
Tom had 2000
Barry had 1200
The confusion could be in "Tom had 2/3 more than Eddie"
Had it said: "Tom had 2/3 of than Eddie" then we needed 2/3 x
with the "more" I interpreted that as 1 2/3 of Eddie's or 5/3 of x
Yes, Tom had $2000
To solve this problem, we can use algebraic equations. Let's assign variables to represent the unknown amounts.
Let's say Barry had an amount represented by "B," Tom had an amount represented by "T," and Eddie had an amount represented by "E."
From the given information, we can write the following equations:
1. Barry had 60% of the amount Tom had:
B = 0.6T (equation 1)
2. Tom had 2/3 more than Eddie:
T = E + (2/3)E (equation 2)
3. The sum of the amounts for all three men is $4400:
B + T + E = 4400 (equation 3)
Let's solve these equations step by step to find the value of T.
Substitute equation 2 into equation 1:
B = 0.6(E + (2/3)E)
Expand the equation:
B = 0.6(E + 2E/3)
Combine like terms:
B = 0.6(3E/3 + 2E/3)
B = 0.6(5E/3)
Multiply by 3/5 on both sides to isolate E:
(3/5)B = (3/5)(0.6)(5E/3)
(3/5)B = E
Now we have the value of E in terms of B:
E = (3/5)B (equation 4)
Substitute equations 1, 3, and 4 into equation 3:
(0.6T) + T + ((3/5)B) = 4400
Combine like terms:
1.6T + (3/5)B = 4400 (equation 5)
Now we have two equations, equation 4 and equation 5, with two unknowns (T and B).
Solve the equations simultaneously to find T.
Substitute equation 4 into equation 5:
1.6T + (3/5)((3/5)B) = 4400
Expand the equation:
1.6T + (9/25)B = 4400
Multiply by 25 on both sides to eliminate the fraction:
25(1.6T) + 25(9/25)B = 25(4400)
40T + 9B = 110,000 (equation 6)
Now we have two equations, equation 4 and equation 6, with two unknowns (T and B).
Let's solve them simultaneously.
Substitute equation 4 into equation 6:
40T + 9((3/5)T) = 110,000
Multiply by 5/3 on both sides to eliminate the fraction:
(5/3)(40T) + (5/3)(9((3/5)T)) = (5/3)(110,000)
(200/3)T + (9/3)T = 5(110,000)
(200T + 27T)/3 = 550,000
(227T)/3 = 550,000
Multiply by 3/227 on both sides to isolate T:
T = (3/227)(550,000)
Calculate the value of T:
T ≈ $7,271.96
Therefore, Tom had approximately $7,271.96.