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Word problem.................GMAT Exam Pack 2

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by Mo2men » Fri Sep 01, 2017 11:36 am
Of 120 hotel rooms rented one night, some were suits rented for $115 each and the rest were double rooms rented for $85 each. If the total revenue from the room rentals ffor this night was $10890, how many suits were rented?

A) 23
B) 35
C) 54
D) 94
E) 99

OA: A
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by Brent@GMATPrepNow » Fri Sep 01, 2017 2:28 pm
Mo2men wrote:Of 120 hotel rooms rented one night, some were suites rented for $115 each and the rest were double rooms rented for $85 each. If the total revenue from the room rentals for this night was $10,890, how many suites were rented?

A) 23
B) 35
C) 54
D) 94
E) 99
We can solve this equation using 1 variable or 2 variables.

Let's use 1 variable.

Let x = # of suites rented
Since 120 rooms were rented in total, 120-x = # of double rooms rented

Suites rented for $115 each
So, revenue from the x suites = 115x

Double rooms rented for $85 each
So, revenue from the 120-x double rooms = 85(120-x)

TOTAL revenue was $10,890
So, 115x + 85(120-x) = 10,890
Expand to get: 115x + 10,200 - 85x = 10,890
Simplify left side: 30x + 10,200 = 10,890
Subtract 10,200 from both sides to get: 30x = 690
Divide both sides by 30 to get: x = 23

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Admin1 » Sat Sep 02, 2017 2:04 pm
The rooms of the hotel are suites or double rooms. The total of rooms is 120.

So we can set:
S+D=120. (equation 1)
where
S - suites
D - double rooms.

The revenue for renting the suites is S*115$ and the revenue for renting the double rooms is D*85$.

The revenue for this night is 10890$. So

S*115$+D*85$=10890$. (equation 2)

From (equation 1) we can get: D=120$-S and introducing D in (equation 2) we will get

S*115$+(120$-S)*85$ = 10890$

S*115$+10200$-S*85$ = 10890$

S*(115$-85$) = 10890$-10200$

S*30$ = 690$

S= (690$/30$)

S = 23

So, this night were rented 23 suites.

PD: we can solve (equation 1) for S, but at the end we will get the number of Double Rooms rented, then we should introduce the value of D in (equation 1) to get the number of suites rented.
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Re: Word problem.................GMAT Exam Pack 2

by Scott@TargetTestPrep » Thu Feb 13, 2020 6:03 am
Mo2men wrote: ↑
Fri Sep 01, 2017 11:36 am
 Of 120 hotel rooms rented one night, some were suits rented for $115 each and the rest were double rooms rented for $85 each. If the total revenue from the room rentals ffor this night was $10890, how many suits were rented?

A) 23
B) 35
C) 54
D) 94
E) 99

OA: A
We let s = the number of suites rented and d = the number of double rooms rented. We can create the equations:

s + d = 120

and

115s + 85d = 10,890

Multiplying the first equation by 115, we have:

115s + 115d = 13,800

Subtracting the second equation from the new equation, we have:

30d = 2910

d = 97

Since s + d = 120 and we know that d = 97, then we have:

s + 97 = 120

s = 23

Answer: A

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