Mike wants to put 150 square feet of artificial turf in his front yard. This is the maximum area of artificial turf allowed by his homeowners association. He wants to have a rectangular area
of turf with length one foot less than 3 times the width. Find the length and width. Round to
the nearest tenth of a foot.

Step-by-step explanation:

Area of the rectangular area = Length * width

A = LW 1

If he wants to have a rectangular area  of turf with length one foot less than 3 times the width, then

L = 3W - 1 2

Substitute 2 into 1

A = (2W-1)W

A = 2W^2 - W

Since area = 150sq.ft

150 = 2W^2 - W

2W^2 - W - 150 = 0

Factorize

2W^2 - W - 150 = 0

W = 1±√1+4(300)/2(2)

W =  1±√1201/2(2)

W = 1±34.655/4

W = 35.655/4

W = 8.91375

W = 8.9 (to nearest tenth)

Get the length

L = A/W

L = 150/8.9

L = 16.85

L = 16.6ft

Hence the length is 16.6ft and the width is 8.9ft

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt