A hotel rents a double-occupancy room for $20 more than a single occupancy room. One night, the hotel took $2965 after renting 15 double-occupancy rooms and 26 single-occupancy rooms?

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Answer 1 · 2018-06-02T23:09:58

See a solution process below:

Let's call the cost of a double occupancy room #d#

Let's also call the cost of a single occupancy room #s#

Given the information in the problem we can write a relationship as:

#d = s + $20#

We can also write:

#15d + 26s = $2965#

We can now substitute #(s + $20)# for #d# in the second equation and solve for #s#

#15d + 26s = $2965# becomes:

#15(s + $20) + 26s = $2965#

#(15 xx s) + (15 xx $20) + 26s = $2965#

#15s + $300 + 26s = $2965#

#15s + $300 - color(red)($300) + 26s = $2965 - color(red)($300)#

#15s + 0 + 26s = $2665#

#15s + 26s = $2665#

#(15 + 26)s = $2665#

#41s = $2665#

#(41s)/color(red)(41) = ($2665)/color(red)(41)#

#(color(red)(cancel(color(black)(41)))s)/cancel(color(red)(41)) = $65#

#s = $65#

If the cost of a single occupancy room is $65

Then the cost of a double occupancy room is #$65 + $20 = color(red)($85)#