Question

country carpets charges $22 per square yard for carpet and an additional installation fee of $100 city carpets charges $25 per square yard for the same carpeting

Answer 1

Solution :

Let 'x' be the number of carpeting done.

From the above question, the equation that we get:

$\implies$ $\huge{\boxed{\sf{22x + 100 = 25x}}}$

Solving,

$\implies$ 22x + 100 = 25x

$\implies$ 22x = 25x - 100

$\implies$ 22x - 25x = -100

$\implies$ -3x = -100

$\implies$ x = -100 / -3

$\implies$ x = 33.33

Therefore,

A person would have to do the carpeting 33.33 times in order to pay the same price for both companies.

Answer 2

Step-by-step explanation:

Let x be the number of square yards of carpeting for which the total cost charged by the two companies will be the same.

We have an expression for the total cost of Country Carpets:

($22/ 1 yd^2)* (x yd^2) + $100

= $22*x+ $100

or 22x+ 100

We also have another expression for the total cost of City Carpets:

($25/ 1 yd^2)* (x yd^2)+ $70

= $25*x+ $70

or 25x+ 70

Now set the two expressions to be equal:

22x+ 100= 25x+ 70

⇒ 100- 70= 25x -22x

⇒ 30= 3x

⇒ 30/3= x

⇒ 10= x