Algebra : Word problems

[Alexandra loves cats]

11 The length of a rectangular field is 30 m greater than its width, which is w meters.

. . .(i) Write down an expression for the area A m² of the field, in terms of w.
. . .(ii) The area of the field is 8,800 m². Find its width and perimeter.

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My working:

11 (i) Length = 30w

. . .L x 30w = A

. . .L x -A = -30w

. . .-LxA = 30w

(ii) 30w x L = 8800

. . .30w = -L + 8800

. . .\(\displaystyle w\, =\, \dfrac{-L}{30}\, +\, \dfrac{8800}{30}\)

. . .\(\displaystyle w\, =\, \dfrac{-L}{30}\, +\, \dfrac{880}{3}\)

. . .\(\displaystyle w\, =\, \dfrac{-L}{30}\, +\, 293.34\)

 

[stapel]

The length of a rectangular field is 30 m greater than its width, which is w meters.

To learn how to translate "thirty more than (this other thing)", try this lesson.

. . .(i) Write down an expression for the area A m² of the field, in terms of w.

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My working:

11 (i) Length = 30w

. . .L x 30w = A

. . .L x -A = -30w

. . .-LxA = 30w

I am going to guess that you're using the variable "x" to stand for "multiplied by". Instead, I'll use a raised dot (or parentheses, or some other standard algebraic notation) to indicate multiplication. So your second and third lines bracket the following "reasoning":

. . . . .\(\displaystyle L\, \cdot \, 30w\, =\, A\)

. . . . .\(\displaystyle \left(L\, \cdot \, 30w\right)\, -\, 30w\, -\, A\, =\, A\, -\, A\, -\, 30w\)

. . . . .\(\displaystyle \left(L\, \cdot \, 30w\right)\, -\, 30w\, -\, A\, =\, \left(\dfrac{L\, \cdot\, 30w}{-30w}\right)(-A)\, \mbox{ and }\, A\, -\, A\, -\, 30w\, =\, \left(\dfrac{A}{-A}\right)(-30w),\, \mbox{ so:}\)

. . . . .\(\displaystyle -L\, \cdot\, A\, =\, -30w\)

But how on earth did you get those two middle lines? What was your reasoning? :shock:

. . .(ii) The area of the field is 8,800 m². Find its width and perimeter.

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My working:

(ii) 30w x L = 8800

. . .30w = -L + 8800

Wasn't the point of solving for L in terms of w the ability then to plug that expression into the equation in place of L, and then solve for a numerical solution?