Solve the Problem $x$ Be the Number of Rock CDs

question 31

Multiple Choice

Solve the problem.
-A recording company is to release 60 new CDs in the categories of rock, country, jazz, and classical. If twice the number of rock CDs is to equal three times the number of country CDs and if the number of jazz CDs is to equal the number of classical CDs, how can the CDs be distributed among the four types? (Let $x$ be the number of rock CDs, $y$ the number of country CDs, $z$ the number of jazz CDs, and $w$ the number of classical CDs. Let $w$ be the parameter.)

• A) \( x=36-w, y=16-w, z=w, 0 \leq w \leq 20 \)
• B) \( x=30-3 w / 5, y=20-2 w / 5, z=w, 0 \leq w \leq 26 \)
• C) \( x=36-6 w / 5, y=24-4 w / 5, z=w, 0 \leq w \leq 30 \)
• D) \( x=30-2 w, y=30-2 w / 5, z=w, 0 \leq w \leq 30 \)

---

Definitions:

Government Ownership

The situation in which assets, enterprises, or industries are owned and operated by the government rather than private individuals or companies.

Mean of Production

Likely a typographic error intended to refer to "Means of Production," which are the resources (such as land, labor, and capital) used to produce goods and services.

Central Planning

An economic system where the government or a central authority makes all decisions regarding the production and distribution of goods and services.

Capitalism

An economic system characterized by private or corporate ownership of capital goods, by investments that are determined by private decision, and by prices, production, and the distribution of goods that are determined mainly by competition in a free market.