Question

Mr. Jones and Mr. Evansbee both have gardens shaped as squares. The length of each side of Mr. Jones’ garden is 6 yd. The length of each side of Mr. Evansbee’s garden is 10 yd.

(a) Write an expression with exponents for the area of Mr. Jones’ garden. Then, find the area of the garden.
(b) Write an expression with exponents for the area of Mr. Evansbee’s garden. Then, find the area of the garden. Each plant takes up 2 yd(squared) of space in both gardens.
(c) How many plants can Mr. Jones place in his garden? How many plants can Mr. Evansbee place in his garden? Explain your reasoning.
(d) For each garden, the cost per plant is $4.99. Using your answers from part (c), how much will each gentleman spend on plants for his garden?

Answers need to be step-by-step please

Answer 1

(a) expression: (6 yd)²; area: 36 yd²

(b) expression: (10 yd)²; area: 100 yd²

(c) Jones: 18; Evansbee: 50

(d) Jones: $89.82; Evansbee: $249.50

Explanation:

You want the area, number of plants that can be placed, and the cost of plantings for gardens that are 6 yards square and 10 yards square. Each plant takes 2 square yards and costs $4.99.

Area of a square

The formula for the area of a square of side length s is ...

A = s²

(a) Jones' garden

The area of a square garden with a side length of 6 yards is ...

A = (6 yd)² . . . . . expression for the area

A = 36 yd² . . . . . the area of the garden

(b) Evansbee's garden

The area of a square garden with a side length of 10 yards is ...

A = (10 yd)² . . . . . expression for the area

A = 100 yd² . . . . . the area of the garden

(c) Number of plants

The area used by the plants is the product of their number and the area taken by each.

For Jones' garden, the number of plants that can be placed is ...

n(2 yd²/plant) = 36 yd²

n = (36 yd²)/(2 yd²/plant) = 18 plants

Mr. Jones can place 18 plants in his garden.

For Evansbee's garden, the number of plants that can be placed is ...

n(2 yd²/plant) = 100 yd²

n = (100 yd²)/(2 yd²/plant) = 50 plants

Mr. Evansbee can place 50 plants in his garden.

(d) Cost of plants

At $4.99 each, the cost of plantings will be $4.99 times the number of plants.

Plants for Jones' garden cost 18($4.99) = $89.82.

Pants for Evansbee's garden cost 50($4.99) = $249.50.