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4 votes
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?​

User Gugelhupf
by
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1 Answer

7 votes

Answer:

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