Group Challenge Problem Discussion

Group Challenge Problem Discussion

Question One

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(2L)(1/10L) = 2 2/10 L

2/10L = 2 2/10

L = 22/10 x 10/2

L = 220/20

Length = 11 and Width = 11/10

Question Two

x(x+2) =15

x^2+2x=15

(x-3)(x+5)

x=3 or x = -5

The shorter side is 3”

Question Three

7 – 4b =< -3(b-1)

7-4b =< -3b+3

7-3 =< -3b+4b

b >= 4

{b| b>= 4}

Question Four

-1/5*2x = -2/5x

-1/5*-25=5

-2/5x+5

And

1/3*4x=4/3x

1/3*9=3

ADD

-2/5x+4/3x=14/15x

5+3=8

14/15x+8 > 1

-8         -8

14/15x > -7

DIVIDE

x > -15/2

Question Five

x+y+z+k=9900

y=x+1/7x

z=(x+y) + 300

k=(x+y+z) + 300

Simplify

7y=7x+x

7y=8x

SIMPLFY

-8x+7y=0

-x-y+z=300

-x-y-z+k=300

x+y+z+k=9900

-x-y-z+k=300

2k=10200

k=5100

x+y+z+5100=9900

-8x+7y=0

-x-y+z=300

x+y+z=4800

ADD

-x-y+z=300

2z=5100

z=2550

x+y+2550=4800

-8x+7y=0

Simplify

x+y = 2250

-8x+7y=0

Find y by multiplying x by 8 gives you

15y=18000

Y=1200

x=1050, y =1200, z= 2550, k =5100

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1. The length of a rectangle is a two-digit number with identical digits (aa). The width is 1/10 of the perimeter, which is 2 times the area of the rectangle. Find the length and the width.
2. How long is the shorter side of a rectangle when one side is 2” longer than the other, and the area is 15 sq. in?
3. Solve the following inequality for b. 7 – 4b ≤ −3(b − 1) Show the solution in set builder notation and interval
4. Solve the following inequality for x. – ¹ (2𝑥 − 25) + ¹ (4𝑥 + 9) > 1                                                                                                                                                                   5                    3
5. Four numbers have a sum of 9900. The second exceeds the first by 1/7 of the first. The third exceeds the sum of the first two by 300. The fourth exceeds the sum of the first three by 300. Find the four