y ≥ 20D) 350x + 200y ≥ 25,000
x + y ≤ 75
x ≤ 15
y ≤ 20Sure, you can pick a number for x and a number for y, plugging-in style. But
then you have to make sure that your x and y follow all those rules laid out in the
problem. And that’s a lot of rules! We find it much easier to take it rule by rule.
Let’s start with that first sentence: CanineCorp makes at least 75 RoboDogs.
Look for the line of each answer choice that involves 75. We can see they all
include “x + y,” which means the total number of iLabs and E-huahuas. So if the
rule says “at least,” this means the sum of the iLabs and E-huahuas must be
greater than or equal to 75. That means we can eliminate answers A and D.
Next, let’s look at our remaining answers, B and C. They look very similar,
except that answer choice B says that x is less than or equal to 15, and y is less
than or equal to 20, while C says the opposite. Which is correct? Head back to
the rules. Where do we see the numbers 15 and 20? “CanineCorp must make at
least 15 iLabs and at least 20 E-huahuas.” So if x is our number of iLabs, it must
be greater than or equal to 15, and same goes for the E-huahuas. Our answer is
C.
Bonus Alegebra: Direct and Inverse Variation
You’ve done such a good job getting through this algebra section, we’ve decided
to reward you with a smidge more algebra. The very last algebraic concepts are
direct and inverse variation. Although you will see only one or possibly two
problems involving these concepts, they are pretty simple once you see how they
work.
When y is directly proportional to x, that means that an equation y = kx can
be written (where k is any constant number). For example, y = 5x is a directly
proportional equation. On the other hand, when y is inversely proportional to x,
then the equation is y = k/x. The equation y = 5/x is an inverse proportion.
x is inversely proportional to , and x is 12 when y is 25. What is y when x is
24?