Question

Task I

John has decided to fix up an old field for his son's horse. The length of the field is
10 meters less than 4 times its width. First, he fenced in the field at a cost of $4.80
per meter. The total cost was $1,584. He now needs to buy sweet grass seed to plant
in the field. The seed costs $3.98 per bag and covers 460 square meters.
How much money will John have invested in this field?​

Answer 1

The total money invested in the field will be
`\$1,623.80`

Explanation:

step 1

Find the dimensions of the field

Let

x -----> the length of the field

y -----> the width of the field

we know that

The perimeter of the field is equal to

`P=2(x+y)`

`P(4.80)=1,584`

`P=330\ m`

so

`330=2(x+y)` ----> equation A

`x=4y-10` ------> equation B

substitute equation B in equation A and solve for y

`330=2(4y-10+y)`

`165=(5y-10)`

`5y=165+10`

`y=35`

Find the value of x

`x=4(35)-10=130`

therefore

The length of the field is 130 meters and the width of the field is 35 meters

step 2

Find the area of the field

The area of the field is

`A=xy`

substitute

`A=(130)(35)=4,550\ m^2`

step 3

Find the number of bags of seed

Divide the area by 460

`4,550/460=9.89\ bags`

Round up to the nearest whole number

`9.89=10\ bags`

step 4

Find the cost of the seed

`(10)(3.98)=\$39.8`

step 5

Find the total money invested in the field

`\$1,584+\$39.8=\$1,623.80`