Math Problem Statement

Julianne is planting a ground cover in one area of her yard. The area she wants to cover is rectan- gular shaped and measures 8.75 ft by 4.5 ft. The manager of the garden shop tells her that she will need to purchase four plants for every square foot of area she wishes to cover. How many plants will she need to buy to complete this project?

Solution

To determine how many plants Julianne will need, we follow these steps:

Step 1: Calculate the area of the rectangular space.

The area AA of a rectangle is given by the formula:

A=length×widthA = \text{length} \times \text{width}

Given:

  • Length = 8.75 ft
  • Width = 4.5 ft

A=8.75×4.5=39.375square feetA = 8.75 \times 4.5 = 39.375 \, \text{square feet}

Step 2: Calculate the number of plants needed per square foot.

The problem states that she needs 4 plants for every square foot of area. So, the total number of plants PP is:

P=39.375×4=157.5P = 39.375 \times 4 = 157.5

Step 3: Round to the nearest whole number.

Since Julianne cannot buy half a plant, we round up to the nearest whole number:

P=158plantsP = 158 \, \text{plants}

Conclusion:

Julianne will need to buy 158 plants to complete her project.

Would you like more details or further clarifications?

Here are 5 related questions:

  1. How would the calculation change if the area were circular?
  2. What if each plant covered a different amount of square footage?
  3. How would the result change if she planted fewer plants per square foot?
  4. What would be the total cost if each plant costs $2.50?
  5. How much area could be covered by a single plant if 4 plants cover 1 square foot?

Tip: Always round up when dealing with practical applications like purchasing materials to ensure full coverage.

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Math Problem Analysis

Mathematical Concepts

Geometry
Multiplication
Area Calculation
Rounding

Formulas

Area of rectangle A = length × width
Total number of plants P = area × plants per square foot

Theorems

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Suitable Grade Level

Grades 5-7