Aluminium Flower
Posted on Thursday, March 19th, 2009 at 2:50 pmalgebra 1 word problems that i have no clue how to solve?
5. A picture which has length 18cm and width 24cm is framed. the total area enclosed by the frame is 720cm^2. Find the dimensions of the frame.
6. James dug a flower bed 5m by 10m. he wished to dig another flower bed with three times the area of the first one by increasing each dimension of the first one by the same number of meters. Find the dimensions of the sencond flower bed.
7. a pan without a top is to be made by cutting squares measureing 3cm on a side from each corner of a swuare piece of aluminium and folding up the sides. find the area of the orignianl piece of aluminium if the volume of the pan is to be 432cm^3.
All three can be solved using the same logic.
5. let the frame width be x. The length and width are each made longer by 2x. Remember that area is l*w.
(2x+18)(2x+24)=720
4x^2 + 84x + 432 = 720
4x^2 + 84x - 288 = 0 There is a factor of 4, so divide everything by 4 to make it easier.
x^2 + 21x - 72 = 0
(x + 24)(x-3) = 0
x + 24 = 0, x = -24 - throw out the negative one
x - 3 = 0, x = 3 This is the width of the frame.
So the dimensions of the frame are 24 x 30
6. The area of the first bed is 50. Three times that is 150. The flower bed dimensions are only increased by x, so
(x+5)(x+10) = 150 - solve like I did in the first one.
x^2+15x+50=150
x^2+15x-100=0
(x + 20)(x-5)=0
x = -20 or x = 5
Throw out the negative answer, x = 5
New bed is 10X15
7. Volume of a rectangular prism is L*W*H. L*W = Area of bottom. Height = 3
So 432/3 = 144. The area of the bottom of the pan is 144. Since it's a square, the dimensions must be 12x12.
There is 3 centimeters off of each end, so add 6 to each dimension to make it 18x18.
Area of 18x18 = 324
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