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

Answer:

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

Step-by-step 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

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