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4 tables and 3 chairs, together, cost ₹ 2250 and 3 tables and 4 chairs cost ₹ 1950. Find the cost of 2 chairs and 1 table.
Given:
4 tables and 3 chairs, together, cost ₹ 2250 and 3 tables and 4 chairs cost ₹ 1950.
To do:
We have to find the cost of 2 chairs and 1 table.
Solution: Let the cost of 1 table and 1 chair be $x$ and $y$ respectively.
According to the question,
$4x + 3y = 2250$.....(i)
$3x + 4y = 1950$.....(ii)
Multiplying equation (i) by 4 on both sides, we get,
$4(4x+3y)=4(2250)$
$16x+12y=9000$.....(iii)
Multiplying equation (ii) by 3 on both sides, we get,
$3(3x+4y)=3(1950)$
$9x+12y=5850$.....(iv)
Subtracting equation (iv) from equation (iii), we get,
$(16x+12y)-(9x+12y)=9000-5850$
$16x-9x+12y-12y=3150$
$7x=3150$
$x=\frac{3150}{7}$
$x=450$
Substituting $x=450$ in equation (ii), we get,
$3(450)+4y=1950$
$1350+4y=1950$
$4y=1950-1350$
$4y=600$
$y=\frac{600}{4}$
$y=150$
$\Rightarrow 2y=2(150)=300$
$x=450$ and $2y=300$
$x+2y=450+300=750$
The cost of 2 chairs and 1 table is Rs. 750.