jackie mows a stip of uniform width around her 25m by 15m rectangular lawn and leaves a patch of lawn that is 60% of the original area. What is the width of the strip?

2(15+2w)w+ 25*2w=.60(15*25)

check that

2x+2=0

To find the width of the strip that Jackie mows around her lawn, we first need to determine the original area of the lawn.

The original area of the rectangular lawn can be calculated by multiplying its length and width. In this case, the length is 25m and the width is 15m, so the original area is:

Original Area = Length * Width = 25m * 15m = 375m²

Now, let's calculate the area of the patch of lawn that Jackie leaves unmowed, which is 60% of the original area. To find this, we can multiply the original area by 0.60:

Area of Patch = Original Area * 0.60 = 375m² * 0.60 = 225m²

Now, we know that Jackie mows a strip of uniform width around the lawn, so the area of this strip can be found by subtracting the area of the patch from the original area. In equation form:

Area of Strip = Original Area - Area of Patch
Area of Strip = 375m² - 225m² = 150m²

Since the width of the strip is uniform, we can use the formula for the area of a rectangle to find its width. The formula for the area of a rectangle is:

Area = Length * Width

In this case, we know the area of the strip is 150m², and the length of the rectangular lawn is reduced by twice the width of the strip (once on each side). So we have:

150m² = (25m - 2w)(15m - 2w)

Expanding this equation:

150m² = 375m² - 50mw - 30mw + 4w²

Combine like terms:

0 = 4w² - 80w + 225

Now we need to solve this quadratic equation for w, the width of the strip. We can use factoring or the quadratic formula to find the solution. Let's use factoring:

0 = (2w - 15)(2w - 15)

Setting each factor equal to zero:

2w - 15 = 0 or 2w - 15 = 0

Solving each equation for w:

2w = 15 2w = 15

w = 15/2 w = 15/2

w = 7.5m w = 7.5m

Since the width cannot be negative, we discard the negative solution. Therefore, the width of the strip that Jackie mows around her lawn is 7.5 meters.

Thanks that seems to have worked the back of my text book says it is 2.1 but i got 2.5 close enough.