Question

Mr. Johnson needs to buy seed for his backyard lawn.

a. If the lawn measures 40 4/5 ft by 50 7/8 ft, how many square feet of seed will he need to cover the entire area?
b. One bag of seed will cover 500 square feet if he sets his seed spreader to its highest setting and 300 square feet if he sets the spreader to its lowest setting. How many bags of seed will he need if he uses the highest setting? The lowest setting?

Answer 1

seed will =
`2075(7)/(10)` ft²

for high setting bag need 5 bags

for low setting bag need 7 bags

Explanation:

given data

lawn length =
`40(4)/(5)` ft

lawn width =
`50(7)/(8)` ft

highest setting = 500 square feet

lowest setting = 300 square feet

to find out

how many square feet of seed will he need to cover the entire area and How many bags of seed will he need if he uses the highest setting and The lowest setting

solution

area = length × width ...............

area =
`40(4)/(5)` ×
`50(7)/(8)`

area =
`(204)/(5)` ×
`(407)/(8)`

area =
`(204*407)/(5*8)`

area =
`(20757)/(10)`

seed will =
`2075(7)/(10)` ft²

and

for high setting bag need

bag need =
`(area)/(high setting)`

bag need =
`(2075)/(500)`

bag need =
`4 (3)/(20)`

so here 4 bag is not sufficient so need 5 bags

and

for low setting

bag need =
`(2075)/(300)`

bag need =
`6 (11)/(12)`

so here 6 bag is not sufficient so need 7 bags

Answer 2

a. He will need
`2,075.7\ ft^2` of seed to cover the entire area.

b. He will need 5 bags of seed if he uses the highest setting and 7 bags of seed if he uses the lowest setting.

Explanation:

a. You can calculate the area of his lawn by multiplying its dimensions.

The dimensions are:

`40(4)/(5)\ ft` by
`50(7)/(8)\ ft`

We can convert the mixed numbers to decimal numbers. To do this,we must divide the numerator by the denominator of the fraction and then we must add the quotient to the whole number part.

Then, these are:

`(40+0.8)\ ft=40.8\ ft`

`(50+0.875)\ ft=50.875\ ft`

Then:

`Area=40.8\ ft*50.875\ ft\\\\Area=2,075.7\ ft^2`

He will need
`2,075.7\ ft^2` of seed to cover the entire area.

b. Let be "h" the number of bags of seed that he will need if he uses the highest setting.

You know that one bag of seed will cover 500 square feet if he uses the highest setting. Then:

`h=(2,075.7\ ft^2)/(500\ ft^2)\\\\h=4.15\\\\h\approx5`

Let be "l" the number of bags of seed that he will need if he uses the lowest setting.

You know that one bag of seed will cover 300 square feet if he uses the lowest setting. Then:

`l=(2,075.7\ ft^2)/(300\ ft^2)\\\\l=6.9\\\\l\approx7`