A box containing 5 red balls and 3 green balls weighs 43 g. When the box contains 3 red balls and 5 red balls it weighs 37g. When it contains one ball of each it weighs 19g. What is the mass of the box and of each ball.

Question

Reiny · Accepted Answer

mass of red --- x
mass of green --y
mass of box ---z

5x + 3y + z = 43
3x + 5y + z = 37
x + y + z = 19

subtract the first two:
2x - 2y = 6
x - y = 3
subtract the last from the first:
4x + 2y = 24
2x + y = 12

Add the two x , y equations:
3x = 15
x = 5
in 2x+y = 12 ---> 10+y = 12
y = 2

in x+y+z = 19
5+2+z=19
z = 12

each red has mass of 5
each green has mass of 2
and the box has mass of 12

Anonymous · Answer

cool thanks

emily · Answer

Thanks! I was struggling a lot with this question and I really appreciate the help!