CHAPTER DRILL ANSWERS AND EXPLANATIONS
Grid-In Drill 1: No Calculator Section
16. 8 Using 3b = 2, solve for b by dividing both sides by 3 to get b = . That means = 4.
Fractional exponents tell you to use the denominator as the root and use the numerator as a
regular exponent. So, = 4. First, cube both sides to find a^2 = 4^3 = 64. Next, take the
square root of both sides to find a = 8.
17. 3 You can solve this question using simultaneous equations because you have two equations
with two variables. First, you need to rearrange the equations a bit: 4x + 2y = 24 divided
by 2 on both sides becomes 2x + y = 12. , multiplied by 2x on both sides, becomes 7y =
14 x. This, divided by 7 on both sides, becomes y = 2x, which can be manipulated into 2x −
y = 0. Now you can add the equations:
2 x + y = 12
+ 2x − y = 0
4 x = 12
Therefore, x = 3.
18. 9 Factor the numerator and the denominator into = 4. The (x − 2) cancels out of
the top and bottom to leave = 4. Multiply both sides by (x − 6) to get x + 3 = 4x −
- Subtract x from both sides: 3 = 3x − 24. Add 24 to both sides: 27 = 3x. Divide by 3 to
get x = 9.
19. 9 This looks suspiciously like a quadratic equation, and if you multiply it out, its equivalent is
b^2 – a^2 . You want to make this as large as possible, so you want b^2 to be large and a^2 to be
small. If b = –3, b^2 = 9; if a = 0, a^2 = 0. So b^2 – a^2 can be as large as 9.
Grid-In Drill 2: Calculator-Permitted Section
32. 3,072
Because the t in n = 12 × represents the number of months, we cannot use the 2 years
time frame given in the question in place of t. The colony has been growing for 24 months,
which is evenly divisible by the 3 in the fractional exponent. The equation is much easier
