BW-BS balls

Adam has a full box of balls that are large or small, black or white. Ratio of large and small balls is 5:3. Within the large balls the ratio of the black to white is 1:2 and between small balls the ratio of the black to white is 1:8

What is the ratio of all black to all white balls?

Result

x =  0.33

Solution:

$\dfrac{a+b}{c+d} = \dfrac{5}{3} \ \\ \dfrac{a}{b} = \dfrac{1}{2} \ \\ \dfrac{c}{d} = \dfrac{1}{8} \ \\ \ \\ a = 1 \ \\ b = 2 \ \\ c = 0.2 \ \\ d = 1.6 \ \\ \ \\ x = \dfrac{ a+b }{c+d} = 0.33 = 1/3 \ \\$

a=1
a+b = 5/3*(c+d)
a = 1/2*b
c = 1/8 * d

a = 1
3a+3b-5c-5d = 0
2a-b = 0
8c-d = 0

a = 1
b = 2
c = 1/5 = 0.2
d = 8/5 = 1.6

Calculated by our linear equations calculator.

Try another example

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. Book read
   If Petra read 10 pages per day, she would read the book two days earlier than she read 6 pages a day. How many pages does a book have?
2. Linear system
   Solve this linear system (two linear equations with two unknowns): x+y =36 19x+22y=720
3. Guppies for sale
   Paul had a bowl of guppies for sale. Four customers were milling around the store. 1. Rod told paul - I'll take half the guppies in the bowl, plus had a guppy. 2. Heather said - I'll take half of what you have, plus half a guppy. The third customer, Na
4. Three days
   During the three days sold in stationery 1490 workbooks. The first day sold about workbooks more than third day. The second day 190 workbooks sold less than third day. How many workbooks sold during each day?
5. Two equations
   Solve equations (use adding and subtracting of linear equations): -4x+11y=5 6x-11y=-5
6. The dormitory
   The dormitory accommodates 150 pupils in 42 rooms, some of which are triple and some are quadruple. Determine how many rooms are triple and how many quadruples.
7. Hotel rooms
   In the 45 rooms, there were 169 guests, some rooms were three-bedrooms and some five-bedrooms. How many rooms were?
8. Factory and divisions
   The factory consists of three auxiliary divisions total 2,406 employees. The second division has 76 employees less than 1st division and 3rd division has 212 employees more than the 2nd. How many employees has each division?
9. Two numbers
   We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers.
10. Theatro
    Theatrical performance was attended by 480 spectators. Women were in the audience 40 more than men and children 60 less than half of adult spectators. How many men, women and children attended a theater performance?
11. Trees
    Along the road were planted 250 trees of two types. Cherry for 60 CZK apiece and apple 50 CZK apiece. The entire plantation cost 12,800 CZK. How many was cherries and apples?
12. Legs
    Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
13. Mushrooms
    Eva and Jane collected 114 mushrooms together. Eve found twice as much as Jane. How many mushrooms found each of them?
14. Elimination method
    Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
15. Antennas
    If you give me two antennas will be same. If you give me again your two antenna I have a 5× so many than you. How many antennas have both mans?
16. Three brothers
    The three brothers have a total of 42 years. Jan is five years younger than Peter and Peter is 2 years younger than Michael. How many years has each of them?
17. Equations - simple
    Solve system of linear equations: x-2y=6 3x+2y=4