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1. There are two squares. The perimeter of the larger square is 24 cm longer than the perimeter of the smaller one, and the area of the larger square is 96 cm^2 more than the area of the smaller one. What is the perimeter of the smaller square in cm?

2. A cowboy agreed to work for one year for 19,200 dollars plus a horse. He quit after 7 months and was paid 10,450 dollars plus a horse. How many dollars was the horse worth, if the paid salary reflects the fair proportion of his yearly salary?

3. For negative numbers a, b, and c, we know that (x-b-c)/a + (x-c-a)/b + (x-a-b)/c = 3. what is x in terms of a, b, and c?

Nov 21, 2020
edited by Guest  Nov 21, 2020

#1
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1. There are two squares. The perimeter of the larger square is 24 cm longer than the perimeter of the smaller one, and the area of the larger square is 96 cm^2 more than the area of the smaller one. What is the perimeter of the smaller square in cm?

Call the side  of the smaller square , x......the perimeter is  4x

Since the perimeter  of the larger is 24 more....its perimeter   = 4x + 24.....and its side is 1/4 of this = x + 6

Area of smaller square  + 96  = Area of larger square

x^2 + 96  = (x + 6)^2       simplify

x^2 + 96 = x^2 + 12x + 36       subtract x^2 from both sides

96  =  12x + 36

96 - 36  = 12x

60  =  12x      divide both sides by 12

5 = x  =side of the  smaller square

Perimeter of smaller square  = 5 * 4   =  20 cm   Nov 21, 2020
#3
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Thank you so much for the answers!

Guest Nov 21, 2020
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2. A cowboy agreed to work for one year for 19,200 dollars plus a horse. He quit after 7 months and was paid 10,450 dollars plus a horse. How many dollars was the horse worth, if the paid salary reflects the fair proportion of his yearly salary?

(7/12)  * 19200  =   11200  =  pay for 7 months

11200  - 10450  =   \$750  =  horse's worth   Nov 21, 2020
#4
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3.

Multiply both sides by abc to get rid of all division parts
−a^2b−a^2c−ab^2+abx−ac^2+acx−b^2c−bc^2+bcx=3abc

"Simplify"
x(ab+ac+bc) = a^2b+a^2c+ab^2+3abc+ac^2+b^2c+bc^2

Factor out x
x(ab+ac+bc) = a^2b+a^2c+ab^2+3abc+ac^2+b^2c+bc^2

Divide both sides by ab+ac+bc

x = (a^2b+a^2c+ab^2+3abc+ac^2+b^2c+bc2)/ab+ac+bc

Hope it helped.

By the way all exponents are alone, meaning they are NOT being multiplied by a variable or being added with other numbers. Sorry if it is confusing.

Nov 21, 2020