Mr Lee has a rectangular plot of land 50 m by 25 4/5 m. Each square metre of grass planted in the land would cost him $60.
(a) How much must Mr Lee pay in order to grass the whole plot of land?
(b) He sold the land at $90 per square metre. How much did Mr Lee receive from selling the land?
To solve this problem, we need to use math operations involving fractions and multiplication.
(a) To find the total area of the land in square metres, we multiply the length by the width:
Area = length x width = 50 m x 25 4/5 m
To convert the mixed fraction to an improper fraction, we multiply the whole number (25) by the denominator (5) and add the numerator (4), then write the result over the denominator:
25 4/5 = (25 x 5 + 4) / 5 = 129/5 m
So, the area is:
Area = 50 m x 129/5 m = 2580 m²
To find the total cost of planting grass on the land, we multiply the area by the cost per square metre:
Total cost = Area x Cost per square metre = 2580 m² x $60/m²
Using a calculator, we get:
Total cost = $154,800
Therefore, Mr Lee must pay $154,800 in order to grass the whole plot of land.
(b) To find the total revenue Mr Lee receives from selling the land, we need to find the area of the land in square metres and then multiply it by the selling price per square metre:
Area = 50 m x 129/5 m = 2580 m²
Total revenue = Area x Selling price per square metre = 2580 m² x $90/m²
Using a calculator, we get:
Total revenue = $232,200
Therefore, Mr Lee receives $232,200 from selling the land.
To find the answers, we need to calculate the area of the rectangular plot of land.
(a) To calculate the area of a rectangle, we multiply the length by the width.
Area = Length x Width
Given:
Length = 50 m
Width = 25 4/5 m
To convert the width into a fraction:
25 4/5 = 25 + 4/5 = 25 + 4/5 = (25 x 5 + 4)/5 = 129/5
Substituting the values into the formula:
Area = 50 m × 129/5 m
Area = (50 × 129) / 5
Area = 6450 / 5
Area = 1290 square meters
To calculate the cost of grassing the whole plot of land, we multiply the area by the cost per square meter.
Cost = Area × Cost per square meter
Given:
Cost per square meter = $60
Substituting the values:
Cost = 1290 square meters × $60
Cost = $77400
Therefore, Mr. Lee must pay $77400 to grass the whole plot of land.
(b) To calculate the total amount received from selling the land, we multiply the area by the selling price per square meter.
Amount received = Area × Selling price per square meter
Given:
Selling price per square meter = $90
Substituting the values:
Amount received = 1290 square meters × $90
Amount received = $116100
Therefore, Mr. Lee received $116100 from selling the land.