# Chapter 7 - Section 7.1 - Systems of Linear Equations in Two Variables - Exercise Set - Page 822: 87

The number of rooms with kitchen facilities are $50$ and the number of rooms without kitchen facilities are $150$.

#### Work Step by Step

Let us assume x to be the number of rooms with kitchen facilities and y to be the number of rooms without kitchen facilities. This gives: Rent for the x rooms with kitchen facilities equal to $\$100x$. Rent for the y rooms without kitchen facilities equal to$\$80y$. The provided data can be represented in the form of equations as follows: $x+y=200$ (I) $100x+80y=17000$ (II) And multiplying equation (I) with $-80$ , we get: $-80x-80y=-16000$ (III) Now add equation (II) and (III) and solve for x as follows: \begin{align} & 100x+80y-80x-80y=17,000-16,000 \\ & 20x=1000 \\ & x=\frac{1000}{20} \\ & x=50 \end{align} Put the value of x in equation (I): \begin{align} & 50+y=200 \\ & y=200-50 \\ & y=150 \end{align} Thus, the number of rooms with kitchen facilities is $50$ and the number of rooms without kitchen facilities is $150$.

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