SOLUTION: A full box of ball bearings weighs 21 pounds. The box plus 1/3 of the ball bearings weighs 9 pounds. How much does the box alone weigh? A) 4 pounds B) 3 pounds C) 5 pounds D) 6

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Question 1190207: A full box of ball bearings weighs 21 pounds. The box plus 1/3 of the ball bearings weighs 9 pounds. How much does the box alone weigh?
A) 4 pounds
B) 3 pounds
C) 5 pounds
D) 6 pounds
E) 2 pounds


Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Let's say there are 90 ball bearings in total.
I picked something that's a multiple of 3, so that 1/3 of it is some whole number.

1/3 of this is (1/3)*90 = 30 ball bearings.

x = weight of the empty box
b = weight of 30 ball bearings
3b = weight of 90 ball bearings
All weight expressions are in pounds.

Based on the given info provided by your teacher, we can form these two equations
x+3b = 21
x+b = 9

Subtract the equations straight down
The x terms cancel and we are left with this equation
2b = 12
It solves to b = 6 after dividing both sides by 2.

We can then say,
x+b = 9
x+6 = 9
x = 9-6
x = 3
Or you could say
x+3b = 21
x+3*6 = 21
x+18 = 21
x = 21-18
x = 3


Answer: B) 3 pounds
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

            You can solve this problem,  as the other tutor has shown in his post.

            Or,  alternatively,  you can solve it mentally,  without using equations. 


The difference between the first case items and the second case items is 2/3 of the box of ball bearings, which weights 21 - 9 = 12 pounds.


Hence, 1/3 of the box of ball bearing weights 6 pounds.


It means that the full box of ball bearings weights 6*3 = 18 pounds (with no box itself),


and the box itself weights 21-18 = 3 pounds.   ANSWER

Solved.



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