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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?

 
 Sep 8, 2021
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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

 
 Sep 8, 2021

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