Question

The owners of an apartment building rent equal numbers of $1-, 2-,$ and 3 -bedroom units. The monthly rent for a 1-bedroom is $\$ 550,$ a 2 -bedroom is $\$ 700,$ and a 3 -bedroom is $\$ 900 .$ If the total monthly income is $\$ 36,550,$ how many of each type of unit are there?

Name: Problem 55, Chapter 2: Elementary and Intermediate Algebra
Uploaded: 2020-04-15T15:55:41-08:00
Duration: 4 min 9 s
Channel: Alanya Huang
Description: The owners of an apartment building rent equal numbers of 1-, 2-, and 3 -bedroom units. The monthly rent for a 1-bedroom is 550, a 2 -bedroom is 700, and a 3 -bedroom is 900 . If the total monthly income is 36,550, how many of each type of unit are there?

   The owners of an apartment building rent equal numbers of $1-, 2-,$ and 3 -bedroom units. The monthly rent for a 1-bedroom is $\$ 550,$ a 2 -bedroom is $\$ 700,$ and a 3 -bedroom is $\$ 900 .$ If the total monthly income is $\$ 36,550,$ how many of each type of unit are there?

Elementary and Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 2, Problem 55

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Solved by Expert Alanya Huang

04/15/2020

Step 1

Since the owners rent equal numbers of 1-, 2-, and 3-bedroom units, we have the same number of each type of unit. Show more…

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The owners of an apartment building rent equal numbers of $1-, 2-,$ and 3 -bedroom units. The monthly rent for a 1-bedroom is $\$ 550,$ a 2 -bedroom is $\$ 700,$ and a 3 -bedroom is $\$ 900 .$ If the total monthly income is $\$ 36,550,$ how many of each type of unit are there?

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Key Concepts

Variable Representation for Equal Quantities

This concept involves recognizing that when several groups are stated to have equal counts, a single variable can be used to represent the common quantity across those groups. It simplifies the problem by reducing multiple unknowns to just one variable.

Formulating a Linear Equation

This concept is about translating the real-world conditions of a problem into an algebraic equation. By multiplying the common variable by the corresponding rates or costs and summing these expressions, a single linear equation that represents the total value or sum is formed.

Solving Linear Equations

Once a linear equation is established, the next step is to solve it using algebraic operations such as combining like terms and isolating the variable. This process involves simplifying the equation so that the value of the variable, which represents the unknown quantity, can be determined.

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