Answer:
1. The system of equations is given as follows;
S + L = $1,300................(1)
S + 2·C = $1,400............(2)
S + L + C = $1,600.........(3)
Where;
S = The cost of a sofa
L = The cost of a love sea
C = The cost of a single chair
2. The cost of a love sea, L is $500
Step-by-step explanation:
1. The given information are;
The price of sofa and love sea = $1,300
The price of sofa and two chairs = $1,400
The price of sofa, love sea, and one chair = $1,600
Let the cost of a sofa = S
Let the cost of a love sea = L
Let the cost of a chair = C
Therefore, we have;
S + L = $1,300................(1)
S + 2·C = $1,400............(2)
S + L + C = $1,600.........(3)
2. From equation (1), we have;
L = $1,300 - S
Similarly, from equation (2),we have;
C = ($1,400 - S)/2
Substituting the values of L and C in equation (3), we have;
S + $1,300 - S + ($1,400 - S)/2 = $1,600
Which gives;
($1,400 - S)/2 = $1,600 - $1,300 = $300
$1,400 - S = 2 × $300 = $600
$1,400 = $600 + S
$600 + S = $1,400
S = $1,400 - $600 = $800
S = $800
The cost of a love seat, L, is given from the relation L = $1,300 - S, above, which gives;
L = $1,300 - $800 = $500
The cost of a love sea, L is $500 .
