Question 1208685: please help me solve:
An advertisement from the back of Denton checklist:
$1300 sofa and love seat
$1400 sofa and two chairs
$1600 sofa, love seat, one chair
HOw much does each piece of furniture cost individually?
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! please help me solve:
An advertisement from the back of Denton checklist:
(1) $1300 sofa and love seat
(2) $1400 sofa and two chairs
(3) $1600 sofa, love seat, one chair
How much does each piece of furniture cost individually?
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From (1) and (3), we see that one chair price is 1600 - 1300 = 300 dollars.
Having it, from (2) we conclude that the sofa price is 1400 - 2*300 = 1400 - 600 = 800 dollars.
Finally, from (1) we deduce that the love seat price is 1300 - 800 = 500 dollars.
ANSWER. The prices are $800 for sofa, $500 for love seat and $300 for a chair.
Solved.
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This problem is intended and is expected to be solved mentally, using reasoning only and without using any equations.
The normal expectation is that a person/ (a student) will solve it mentally in his/her mind from the first glance,
using paper and pencil and spending about 1 minute to make all necessary calculations and writing.
If the solution does not teach it, then this time is wasted.
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
x = sofa's price
y = love seat's price
z = chair's price
Each price is in dollars.
The various combo prices in the instructions gives us this system of equations.
Since x+y = 1300, we can replace the x+y in the 3rd equation with 1300
So,
x+y+z = 1600
x+y+z = 1600
1300+z = 1600
z = 1600-1300
z = 300
Put another way: subtract equations (3) and (1) to end up with z = 300.
Use this value of z to find x in the 2nd equation
x+2z = 1400
x+2*300 = 1400
x+600 = 1400
x = 1400-600
x = 800
Then use the 1st equation to find y.
x+y = 1300
800+y = 1300
y = 1300-800
y = 500
Answers:
Sofa = $800
Love Seat = $500
Chair = $300
I'll let the student check these answers.
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