16. 28 Let s equal the number of staples required by the students and let p be the number of
popsicle sticks required. If the number of staples the students will need is three times the
number of popsicle sticks they will need, then s = 3p. If the students need 84 staples for this
project, then s = 84. Substitute 84 for s to get 84 = 3p. Divide both sides by 3 to get 28 = p.
The students will need 28 popsicle sticks.
17. 0 If a parabola intersects the x-axis at the points (5, 0) and (–5, 0), it must be symmetric about
the x-axis and centered at x = 0. The x-coordinate of its vertical axis of symmetry must then
be 0.
18. 94 The question describes a 100-meter ramp that forms a triangle. The length of this ramp
corresponds to the hypotenuse of a triangle. The height of the ramp is the length of the side
of the triangle opposite the 20° angle; the horizontal distance from the start of the ramp
immediately below the entrance of the mall is the side of the triangle adjacent to the 20°
angle. The function that relates adjacent and hypotenuse is cosine: cos θ = . In
this problem, cos 20° = , where x is the horizontal distance. Solve by multiplying both
sides by 100: cos 20° = x. Next, replace cos 20° with the value given in the problem,
0.939: 100(0.939) = x. Multiply 100 by 0.939 to get x = 93.9, which rounds to 94.
19. 7 Let x equal the number. Then, 2x = x − 5 Þ x = –5. Three times that number plus seventeen
minus that number is 3(–5) + 17 – (–5) = 7.
20. 3 x^2 + 2x − 8 = (x + 2)(3x − 4) = 0. Solving x + 2 = 0 and 3x − 4 = 0 for x, we find that the
two solutions for x are –2 and . The question asks us to subtract the value of the smaller
solution from the larger solution. This difference is .
Section 4: Math (Calculator)
1. B To solve this question, simply subtract y from both sides of the equation to get 2y = 2,
which is (B).
2. A Whenever the question includes variables, plug in. If m = 2, then Merry would pay the one-
time enrollment fee plus 2 months’ worth of monthly fees, which is 50 + 15(2) = 80. Plug in
2 for m in the answer choices to see which answer equals the target number of 80. In (A),
15(2) + 50 = 80. This is the target number, so leave this answer, but be sure to check the
other choices just in case. In (B), 15 + 50(2) = 115. In (C), 15(2) – 50 = –20, and in (D),
(15 + 50)(2) = 130. Since none of the other answer choices equals the target number, the
