4 stools cost as much as 3 chairs. 5 stools cost $28 more than 2 chairs. How much do 2 stools and 2 chairs cost?
+313 Let the cost of 1 chair = x
∴ Cost of 3 chairs = 3x
Since Cost of 4 stools = Cost of 3 chairs.
∴ Cost of 4 stools = 3x
∴ Cost of 1 stool = \( {3x\over 4}{}{}\).........(1)
Cost of 2 chairs = 2x
Since the cost of 5 stools is $28 more than 2 chairs.
∴ Cost of 5 stools = 2x + 28
∴ Cost of 1 stool = \({2x+28\over 5}{}{}\)............(2)
From equations (1) and (2) we have,
Cost of 1 stool = \( {3x \over 4}{}{}\)
Cost of 1 stool = \({2x+28 \over 5}\frac{}{}\)
∴ \( {3x\over 4}{}{} = {2x+28\over5}\)
⇒ 15x = 8x + 112
⇒ 7x = 112
⇒ x = 16
∴ Cost of 1 chair = $16
And Cost of 1 Stool = \( {3x \over 4}{}{} = {3\over4} * 16 = 12\)
Now we have,
Cost of 1 chair = $16
∴ Cost of 2 chairs = 2 × $16 = $32
Cost of 1 stool = $12
∴ Cost of 2 stools = 2 × $12 = $24
Hence the cost of 2 chairs and 2 stools = $32 + $24 = $56
∴ The cost of 2 chairs and 2 stools = $56
