3.3: The Fixer Upper

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INTRODUCTION

Recall the work done in Preparation 3.3 to calculate length, area, and volume. Read the definitions below for a quick refresher.

Length is the amount of much space an object takes up in one dimension. For example, a standard computer keyboard has a length of about 22 inches.

Area is how much space an object takes up in two dimensions. In other words, the size of the surface of a two-dimensional object. For example: If a table top is 2 feet long and 3 feet wide, the area is 2 ft * 3 ft = 6 feet squared.

Volume is how much space an object takes up in three dimensions. In other words, it's the amount of space inside a three-dimensional object. For example, if a storage box is 5 feet long, 3 feet wide, and 2 feet deep, then its volume is 5 ft * 3 ft * 2 ft = 30 feet cubed

Imagine a house and the small piece of land that surrounds the house. A small piece of land that can be purchased or sold is often called a lot.

Figure 1 (House and Lot): This scale drawing shows the rectangular lot (dark border), the house (dark shade near the middle), and the driveway (near the bottom left). The shaded area to the back of the house (right side of the figure) represents the backyard that is to be reseeded.

Scale drawing showing the House and lot, indicating the following scale:
1 square = 10 feet
2 squares = 20 feet
3 squares = 30 feet

In this collaboration, you are going to be thinking about and making sense of the scale drawings. With reference to the scale drawing, consider the questions below in your group:

(a) What are the dimensions of the lot?

(b) How many square feet are in the house?

(d) What is the area of the lot?

(e) What percentage of the lot is covered by the house?

SPECIFIC OBJECTIVES

By the end of this collaboration, you should understand that

formulas can be found by searching the Internet and reference books.
a variable can be used to represent an unknown.
using a formula requires knowing what each variable represents.

By the end of this collaboration, you should be able to

use formulas from geometry and perform calculations that involve rates and measures to support financial decisions.
evaluate an expression.
use the appropriate units for length, area, and volume.

PROBLEM SITUATION: HOME IMPROVEMENTS

Bob and Carol Mazursky have purchased a house and the small piece of land that surrounds the house. (A small piece of land that can be purchased or sold is often called a lot.) Bob and Carol want to make some improvements to their new property. In the following few problems, you will calculate the costs of these improvements. Scale drawings of the house and the lot are displayed after the problems. You will need these drawings to calculate improvement costs.

(1) Review the drawing of the house and lot (Figure 1). What does the scale mean?

(2) Bob and Carol want to get the backyard (Figure 1) fertilized and reseeded. They found an ad for Gerry’s Green Team lawn service, which can be seen here:

Gerry's Green Team flyer. Grass seed = 4 pounds per 1000 sg ft at !1.25 per pound. Fertiziler: 50 pounds per 12000 sq ft at $0.50 per pound. Labor: 4 hours at $45 per hour.

Gerry came to their house and said that the job would take about half a day and would cost about $600. Is Gerry’s estimate consistent with his advertisement? Why or why not?

(3) There is a brick grill in the backyard. Bob and Carol are going to make a concrete patio in the shape of a trapezoid next to the grill (Figure 2). The concrete slab needs to be at least 2 inches thick. They will use 40-pound bags of premixed concrete. Each 40-pound bag makes 0.30 cubic feet of concrete and costs $6.50. How much will the materials cost, including the 7.5% tax?

Outdoor Grill: Bob and Carol are going to add a trapezoidal patio adjacent to the outdoor grill in the backyard. The shaded area is made of concrete and two inches deep.

Figure 2

Scale drawing showing the patio and grill, indicating the following scale:
1 square = 1 foot

MAKING CONNECTIONS

Record the important mathematical ideas from the discussion.

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