Problem Solving

One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?
(A) 18
(8) 16
(C) 12
(D) 8
(E) 4

Here's an algebraic approach:

Monday: trucks in lot = 20

Let R = # of trucks rented out from Tuesday to Friday.
So, # of trucks remaining in lot = 20 - R

50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning
In other words, R/2 trucks (half) were returned

Saturday: trucks in lot = (20 - R) + R/2
= 20 - R/2

There were at least 12 trucks on the lot that Saturday
So, 20 - R/2 > 12 ....solve for R
Rearrange to get: 20 - 12 > R/2
Simplify to get: 8 > R/2
Multiply both sides by 2 to get: 16 > R
Since R is less than or equal to 16, the maximum value of R is 16

Answer: B

Cheers,
Brent

oquiella wrote:One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?


A. 18
B. 16
C. 12
D. 8
E. 4

We are given that a truck rental lot had a total of 20 trucks, that 50% of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and that at least 12 trucks were on the lot that Saturday morning.

We can let t = the total number of trucks rented. Then, (20 - t) trucks were not rented at all. Since 0.5t of the trucks were returned, there were (20 - t) + 0.5t = 20 - 0.5t trucks on the lot Saturday morning. Thus, we can create the following inequality:

20 - 0.5t ≥ 12

8 ≥ 0.5t

16 ≥ t

We see that the greatest possible value of t is 16.

Answer: B

One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?
(A) 18
(8) 16
(C) 12
(D) 8
(E) 4

Here's an algebraic approach:

Monday: trucks in lot = 20

Let R = # of trucks rented out from Tuesday to Friday.
So, # of trucks remaining in lot = 20 - R

50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning
In other words, R/2 trucks (half) were returned

Saturday: trucks in lot = (20 - R) + R/2
= 20 - R/2

There were at least 12 trucks on the lot that Saturday
So, 20 - R/2 > 12 ....solve for R
Rearrange to get: 20 - 12 > R/2
Simplify to get: 8 > R/2
Multiply both sides by 2 to get: 16 > R
Since R is less than or equal to 16, the maximum value of R is 16

Answer: B

Cheers,
Brent