SOLUTION: An antique dealer sold four chairs for a total of �800. The Regency chair went for as much as the Victorian chair and half the Edwardian chair. The Victorian chair went for as much

Question 151281: An antique dealer sold four chairs for a total of �800. The Regency chair went for as much as the Victorian chair and half the Edwardian chair. The Victorian chair went for as much as the Queen Anne minus the cost of the Edwardian. The Edwardian sold for one-third of the price of the Regency, the Queen Anne went for the total raised by the Victorian and the Edwardian. How much was each chair?
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An antique dealer sold four chairs for a total of �800. The Regency chair went for as much as the Victorian chair and half the Edwardian chair. The Victorian chair went for as much as the Queen Anne minus the cost of the Edwardian. The Edwardian sold for one-third of the price of the Regency, the Queen Anne went for the total raised by the Victorian and the Edwardian. How much was each chair?
:
The total cost of the 4 chairs equation:
R + V + E + Q = 800
:
Write an equation for each statement:
:
"The Regency chair went for as much as the Victorian chair and half the Edwardian chair."
R = V + E
;
"The Victorian chair went for as much as the Queen Anne minus the cost of the Edwardian."
V = Q - E
:
"The Edwardian sold for one-third of the price of the Regency,"
E = R
:
"the Queen Anne went for the total raised by the Victorian and the Edwardian."
Q = V + E
:
Try to get each variable in terms of R:
:
Utilizing the two equations: R = V + E and E = R
R = V + *R
R = V + R
R - R = V
V = R
:
Q = V + E
Substitute for V & E
Q = R + R
Q = R + R
Q = R
:
Substitute for E,V,Q in the total cost equation:
R + R + R + R = 800
Multiply by 6 to get rid of the denominators:
6R + 2R + 5R + 7R = 6(800)
20R = 4800
R =
R = 240, cost of the Regency Chair
;
E = R
E = 240
E = 80, cost of Edwardian Chair
:
Q = R
Q = 240
Q = 280, cost of the Queen Ann chair
:
V = R
V = 240
V = 200, cost of the Victorian Chair
:
you can check these, add them up, confirm they = 800

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