19. or 3.66 or 3.67
Whenever there are two equations with the same two variables, the equations can be solved
simultaneously by adding or subtracting them. Take the second equation and rewrite it so
that the variables are on the left side of the equation: 17r + 22v = 63. Stack the equations
and add them together.
13 r + 8v = 47
17 r + 22v = 63
30 r + 30v = 110
Divide the entire equation by 30 to get r + v = . This is too big to grid in, so reduce it to
.
20. 2 The area of the current plot is 4 × 6 = 24 square feet, so the new plot will be 24 × 2 = 48
square feet. According to the question, x feet will be added to each side to obtain the new
area of 48 feet. Since the length is only 2 feet more than the width, you need two factors of
48 that differ by 2. You may recognize that these factors are 6 and 8. So, the increase was 2
feet in each direction. Alternatively, you can write a quadratic: (4 + x)(6 + x) = 48. Expand
the right side of the equation to get x^2 + 10x + 24 = 48. Set the equation to 0 by subtracting
48 from both sides to get x^2 + 10x − 24 = 0. Factor the equation to get(x + 12)(x − 2) = 0.
Therefore, x = –12 or x = 2. Since lengths can never be negative the only possible value is
x = 2. The correct answer is 2.
Section 4: Math (Calculator)
1. C Use Process of Elimination. According to the question, P represents the population, so the
outcome of the entire equation has something to do with the population. Therefore,
eliminate both (A) and (B) because 1.0635 can’t represent the population if P does. In the
given equation, the only operations are multiplication and addition, which means that over
time the population would increase. Therefore, eliminate (D). The correct answer is (C).
2. B To solve the quadratic equation, first set the equation equal to 0. The equation becomes x^2 +
12 x − 64 = 0. Next, factor the equation to get(x + 16)(x − 4) = 0. Therefore, the two
possible solutions for the quadratic equation are x + 16 = 0 and x − 4 = 0, so x = –16 or 4.
Since the question states that x > 0, x = 4 is the only possible solution. Another way to
approach this question is to plug in the answers. Start with (B), x = 4. Plug 4 into the
equation to get 4^2 + 12(4) = 64. Solve the left side of the equation to get 16 + 48 = 64, or 64
= 64. Since this is a true statement, the correct answer is (B).
3. A To figure out the total number of shelving units Sai could use, find the total available wall
space and divide by the length of the units. The total amount of wall space can be calculated
as 119 – 21. Because the length of each unit is 7 feet, the maximum number of units Sai
