jugoslav

Alex, Justin, and Roy shared a sum of money. Alex received 1/2 of the total share of Justin and Roy. Justin received 1/3 of the total share of Alex and Roy. If Roy received $180 more than Justin, how much was the sum of money they shared?

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A + J + R = x

A = x/3

J = x/4

R = x/4 + 180

x = x/3 + x/4 + (x/4 + 180)

x = 1080  

Abel had 3 times as many books as Thomas. Abel donated 1/4 of his books to charity. What was the ratio of the number of books Thomas had to the number of books Abel had in the end?

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A : T = 3 : 1       or     3x : x

3x - (3x/4) = 2.25x

T : A = 1 : 2.25      or     4 / 9

x + 2x + 5x = 180           x = 22.5

The angles are 22.5º, 45º, and 112.5º 

The correct question would be:

In the diagram below AM = BM = CM,  and angle BMC + angle A = 201 degrees.  Find angle B in degrees.

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Angle AMC = x

(180 - x) + 1/2(180 - x) = 201

x = 46

∠B = 46 / 2 = 23º

Area = 234 cm² 

A wooden block has rectangular faces and sides of lengths L, W, and H. The faces have areas of 18.7 cm², 38.5 cm², and 23.8 cm² as shown. Find the lengths of the sides. 

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W * L = 38.5

W * H = 18.7

L * H = 23.8

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W = 18.7 / H

L = 23.8 / H

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W * L = 38.5

(18.7 / H)(23.8 / H) = 38.5

H = 3.4 cm

W = 18.7 / H = 5.5 cm

L = 38.5 / W = 7 cm

Matt, Justin, Tony, and Gabriel shared $168. Gabriel received 1/7 of the amount of money received by Matt, Tony, and Justin. Matt received 3/4 of the amount of money received by Tony and Justin. Justin received 2/5 as much money as Tony. How much did Justin receive?

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M + J + T + G = 168

M+J+T => X

X + X/7 = 168             X = 147

Gabriel received =>    168 - 147 = 21

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M + J + T = 147

J + T => Y

Y + 3Y/4 = 147           Y = 84

Matt received =>     147 - 84 = 63

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J + T = 84

T + 2T/5 = 84            T = 60

Justin received =>     84 - 60 = 24   

Radius = 4√13

In trapezoid PQRS, Base PQ is parallel to base RS. Let point X  be the intersection of diagonals PR and QS. The area of triangle PQX is 20 and the area of triangle RSX is 48.  Find the area of trapezoid PQRS.

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[PQRS] = (√20 + √48)²