Question

Two chairs and a table can b bought for 170.Five chairs and four tables can b bought for 530 .Find the cost of a chairs

Answer 1

$\bold{given : } \\ \\ 2 \: chairs \: and \: 1 \: table \: for \: rs \: 170 \\ \\ 5 \: chairs \: and \: 4 \: tables \: for \: rs \: 530 \\ \\ \\ \\ \bold{let : } \\ \\ cost \: for \: 1 \: chair \: : \\ \\ = > \: x \: rs \: \\ \\ cost \: for \: 1 \: table \: : \\ \\ = > \: y \: rs \: \\ \\ \\ \\ \bold{according \: to \: conditions : } \\ \\ \bold{2x + y = 170 }........................1\\ \\ \bold{5x + 4y = 530} .....................2\\ \\ \\ \\ \bold {multiply \: equation \: 1 \: by \: 4 }\\ \\ 4(2x + y = 170) \\ \\ \bold{8x + 4y = 680}......................3 \\ \\ \\ \\\bold {substract \: equation \: 2 \: from \: 3} \\ \\ 8x + 4y = 680 \\ - \\ 5x + 4y = 530 \\ - - - - - - - \\ 3x = 150 \\ \\ x = \frac{150}{3} \\ \\ \bold{x = 50 \: rs} \: \\ \\ \\ \\ \bold {put \: x = 50 \: in \: equation \: 1} \\ \\ 2x + y = 170 \\ \\ 2 \times 50 + y = 170 \\ \\ 100 + y = 170 \\ \\ \bold{y = 70 \: rs \: } \\ \\ \\ \\ \bold{cost \: for \: 1 \: chair \: is \:\: rs \: \:50} \\ \\ \bold{cost \: for \: 1 \: table \: is \:\: rs \:\: 70}$