16 questions were answered correctly.
2 questions were answered incorrectly.
1
Abby can buy individual songs for $1.00 to download, or she can
download an entire album for $8.00. Abby can spend no more
than a total of $50. She wants to buy at least two albums, and no
more than 30 individual songs.
The following system of inequalities represents this situation,
where x is the number of individual songs and y is the number of
albums.
x + 8y ≤ 50
x ≤ 30
y≥2
Which blue shaded region corresponds to Abby’s possible
choices?
, UNIT 3 — MILESTONE 3
16/18
, UNIT 3 — MILESTONE 3
16/18
RATIONALE
The given situation can be
expressed with these
inequalities. To find the area that
represents the solution, we will
need to graph each inequality.
Let's start with x + 8y ≤ 50. To
graph this inequality, we need to
graph it as a line. We can do this
by finding the x and y intercepts.
The x intercept is the coordinate
point when y = 0. When
substituting this value in for y,
we get an x intercept of (50,0).
The y intercept is the coordinate
point when x = 0. When
substituting this value in for x,
we get a y intercept of (0,6.25).
Next, plot these two points and
graph the line.
, This is the graph of the line that
UNIT 3 — MILESTONEcontains
3 the points (0,6.25) and
(50,0). Next, we need to graph
this as an inequality. Since Abby
wants to spend only up to 16/18
50 dollars, we will shade
everything BELOW the line.
This represents the inequality x
+ 8y ≤ 50. Now, we can graph
the other two inequalities, x ≤ 30
and y ≥ 2.
For the inequality x ≤ 30, this
tells us that Abby wants to buy
no more than 30 individual
songs. This is represented with
a line at x = 30 and we will
shade BELOW, or to the LEFT, of
the line.
For the inequality y ≥ 2, this tells
us that Abby wants to buy at
least 2 albums. This is
represented with a line at y = 2
and we will shade ABOVE the
line.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Topscorer. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $13.99. You're not tied to anything after your purchase.
