Question

I need help with the entire problem. The question is about a sketchy hotel.

Answer 1

Let d and s be the cost of a double and single- occupancy room, respectively. Since a double-occupancy room cost $20 more than a single room, we can write

`d=s+20\ldots(A)`

On the other hand, we know that 15 double-rooms and 26 single-rooms give $3088, then, we can write

`15d+26s=3088\ldots(B)`

Solving by substitution method.

In order to solve the above system, we can substitute equation (A) into equation (B) and get

`15(s+20)+26s=3088`

By distributing the number 15 into the parentheses, we have

`15s+300+26s=3088`

By collecting similar terms, it yields,

`41s+300=3088`

Now, by substracting 300 to both sides, we obtain

`41s=2788`

then, s is given by

`s=(2788)/(41)=68`

In order to find d, we can substitute the above result into equation (A) and get

`\begin{gathered} d=68+20 \\ d=88 \end{gathered}`

Therefore, the answer is:

`\begin{gathered} \text{ double occupancy room costs: \$88} \\ \text{ single occupancy room costs: \$68} \end{gathered}`