SOLUTION: The average cost of 3 handbags is $46.70. The second handbag costs 3 times as much as the first handbag. The third handbag costs $15.30 less than the second handbag. Find the diffe

Algebra ->  Average -> SOLUTION: The average cost of 3 handbags is $46.70. The second handbag costs 3 times as much as the first handbag. The third handbag costs $15.30 less than the second handbag. Find the diffe      Log On


   

Question 614418: The average cost of 3 handbags is $46.70. The second handbag costs 3 times as much as the first handbag. The third handbag costs $15.30 less than the second handbag. Find the difference in cost between the first and third handbags.
Found 2 solutions by richwmiller, Charles1947:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
(x+y+z)/3=4670;
y=3x;
z=y-1530;
a=z-x

a = 2910, x = 2220, y = 6660, z = 5130

Answer by Charles1947(18) About Me  (Show Source):
You can put this solution on YOUR website!
Cost of 1st handbag=x
Cost of 2nd handbag=y
Cost of 3rd handbag=z
%28x%2By%2Bz%29%2F3=46.70
x+y+z=46.70x3=140.10
y=3x
z=y-15.30
We have three equations and three unknowns
substitute 3x for y we get z = 3x-15.30
also x + 3x + z =140.10 or 4x + z = 140.10 or z=140.10-4x
z=3x-15.30 and z=140.10-4x so
3x-15.30=140.10-4x
combine like terms
7x=155.40
divide each side by 7
x=22.20
y=3x22.20=66.60
z=66.60-15.30=51.30
difference between the first and third is 51.30-22.20=29.10