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# Algebra Word Problems

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So I'm in algebra class, and I figured out that I'm really stupid at Algebra but smart at Science. Have no idea how that's possible. But please help with this proportion word problem and this other word problem I can't seem to figure out.

The ratio of boys to girls in a class is 4 to 3, and there is a total of 28 students. How many girls are in the class?

The width of a rectangle is 4 cm less than the length. If each dimension were increased by 3 cm, the width of the new rectangle formed would be two thirds the length of the new rectangle. Find the dimensions of the original rectangle.

Please show all work. Thank you so much!!

Thanks again,

Indian Tech Support

MrPatel  Jan 10, 2018
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Girls  =  (3)  / (4 + 3)  * 28  =    (3/7) * 28  =  3 * (28/7)  =  3 * 4  =  12

The width of a rectangle is 4 cm less than the length. If each dimension were increased by 3 cm, the width of the new rectangle formed would be two thirds the length of the new rectangle. Find the dimensions of the original rectangle.

Let the oiginal length  = L

Let the original width = W =  L  - 4

When  each dimension is increased by 3  we have the following dimensions :

New W = (L - 4) +  3    =  L -  1    and   New L  =     L + 3

So...the new width is (2/3)  the new length

So

L -  1  =  (2/3) (L + 3)       simplify

L - 1    (2/3)L + 2        add 1 to both sides, subtract (2/3)L from both sides

(1/3)L  =  3     multiply both sides by 3

L  =  9 cm  =  original length

L - 4  =  W =  9 - 4   =  5 cm  = original width

CPhill  Jan 10, 2018

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