jugoslav

An isosceles triangle with equal sides of 5 inches and a base of 6 inches is inscribed in a circle. What is the distance between the center of the circle and the base?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

BC = 5      MC = 3         BN = 2.5

BM = sqrt(5² - 3²)

BM / BC = BN / BO        BO = 3 ¹/₈

OM = BM - BO = ⁷/₈

D : R = 8 : 1

8x = x + 42

x = 6

Darius has 48 erasers.

A = 12[sqrt(13² - 12²)]

cos(C + A) = - 0.6

Alan      Barry

3/5x = 4/5(3/4x)        (So far I got only this)

Can someone explain the meaning of this: 

If Barry gave Alan 30, then he would have 100 more than the amount he had left. 

The ratio of the number of magnets Aspilla and Barry had was 2 : 3. When Aspilla bought 4 more magnets and Barry bought 13 more magnets, the ratio became 1 : 2. Find the number of magnets Barry had in the end.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A : B = 2 : 3

(2x + 4) : (3x + 13) = 1 : 2

4x + 8 = 3x + 13

x = 5

Barry had 28 magnets.

1/7 of 35 = 5

So, the concentration of krill would drop to 30/m³

Bryan and Harold had 108 marbles altogether. Bryan gave away 1/2 as many marbles as Harold gave away. The number of marbles Harold had left was the same as the number of marbles he had given away. If Harold had 1/2 as many marbles left as Bryan, how many marbles did Harold have at first?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

B + H = 108

B gave = 1/2x marbles

H gave =  x  marbles

H had left x  marbles

B had left 2x marbles

1/2x + x + x + 2x = 108

x = 24

Harold had 48 marbles 

x + 4 : 3x + 3 = 1 : 2

x = 5

Hannah had 18 apples

A basket contains some white, red, and black balls. There are 15 white and red balls. There are 18 red and black balls. The number of black and white balls is 9. Find the number of balls for each color.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

w + r = 15           w = 15 - r          15 - r + 18 - r = 9         r = 12

b + r = 18            b = 18 - r

w + b = 9

w = 3            r = 12         b = 6