Sat practice Test #8 Answer Explanations

Choice C is correct. Let x represent the number of 2-person tents
and let y represent the number of 4-person tents. It is given that the 
total number of tents was 60 and the total number of people in the 
group was 202. This situation can be expressed as a system of two 
equations, x + y = 60 and 2x + 4y = 202. The first equation can be 
rewritten as y = −x + 60. Substituting −x + 60 for y in the equation
2x + 4y = 202 yields 2x + 4(−x + 60) = 202. Distributing and combining 
like terms gives −2x + 240 = 202. Subtracting 240 from both sides 
of −2x + 240 = 202 and then dividing both sides by −2 gives x = 19. 
Therefore, the number of 2-person tents is 19.
Alternate approach: If each of the 60 tents held 4 people, the total 
number of people that could be accommodated in tents would be 240. 
However, the actual number of people who slept in tents was 202. The 
difference of 38 accounts for the 2-person tents. Since each of these 
tents holds 2 people fewer than a 4-person tent, 38 
_ 
2 = 19 gives the 
number of 2-person tents.

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Choice A is incorrect. This choice may result from assuming exactly 
half of the tents hold 2 people. If that were true, then the total number 
of people who slept in tents would be 2(30) + 4(30) = 180; however,
the total number of people who slept in tents was 202, not 180.
Choice B is incorrect. If 20 tents were 2-person tents, then the 
remaining 40 tents would be 4-person tents. Since all the tents were 
filled to capacity, the total number of people who slept in tents would be 
2(20) + 4(40) = 40 + 160 = 200; however, the total number of people who 
slept in tents was 202, not 200. Choice D is incorrect. If 18 tents were 
2-person tents, then the remaining 42 tents would be 4-person tents. 
Since all the tents were filled to capacity, the total number of people 
who slept in tents would be 2(18) + 4(42) = 36 + 168 = 204; however,
the total number of people who slept in tents was 202, not 204.
QUESTION 11